PERMETRICS Library

permetrics.utils package

• permetrics.utils.classifier_util module
  • calculate_accuracy_score()
  • calculate_class_support()
  • calculate_confusion_matrix()
  • calculate_roc_curve()
  • calculate_single_label_metric()
• permetrics.utils.cluster_util module
  • calculate_adjusted_rand_score()
  • calculate_ball_hall_index()
  • calculate_banfeld_raftery_index()
  • calculate_beale_index()
  • calculate_calinski_harabasz_index()
  • calculate_completeness_score()
  • calculate_czekanowski_dice_score()
  • calculate_davies_bouldin_index()
  • calculate_dbcv_score()
  • calculate_det_ratio_index()
  • calculate_duda_hart_index()
  • calculate_dunn_index()
  • calculate_entropy_score()
  • calculate_f_measure_score()
  • calculate_fowlkes_mallows_score()
  • calculate_gamma_score()
  • calculate_gplus_score()
  • calculate_hartigan_index()
  • calculate_homogeneity_score()
  • calculate_hubert_gamma_score()
  • calculate_jaccard_score()
  • calculate_ksq_detw_index()
  • calculate_kulczynski_score()
  • calculate_log_det_ratio_index()
  • calculate_mc_nemar_score()
  • calculate_mean_squared_error_index()
  • calculate_mutual_info_score()
  • calculate_normalized_mutual_info_score()
  • calculate_phi_score()
  • calculate_precision_score()
  • calculate_purity_score()
  • calculate_r_squared_index()
  • calculate_rand_score()
  • calculate_recall_score()
  • calculate_rogers_tanimoto_score()
  • calculate_russel_rao_score()
  • calculate_silhouette_index()
  • calculate_sokal_sneath1_score()
  • calculate_sokal_sneath2_score()
  • calculate_sum_squared_error_index()
  • calculate_tau_score()
  • calculate_v_measure_score()
  • calculate_xie_beni_index()
  • compute_BGSS()
  • compute_TSS()
  • compute_WG()
  • compute_WGSS()
  • compute_barycenters()
  • compute_clusters()
  • compute_conditional_entropy()
  • compute_confusion_matrix()
  • compute_contingency_matrix()
  • compute_entropy()
  • compute_nd_splus_sminus_t()
  • sum_comb()
• permetrics.utils.data_util module
  • format_classification_data()
  • format_external_clustering_data()
  • format_internal_clustering_data()
  • format_regression_data_type()
  • format_y_score()
  • get_regression_non_zero_data()
  • get_regression_positive_data()
  • is_unique_labels_consecutive_and_start_zero()
• permetrics.utils.encoder module
  • LabelEncoder
    • LabelEncoder.fit()
    • LabelEncoder.fit_transform()
    • LabelEncoder.inverse_transform()
    • LabelEncoder.transform()
• permetrics.utils.regressor_util module
  • calculate_absolute_pcc()
  • calculate_ec()
  • calculate_entropy()
  • calculate_mse()
  • calculate_nse()
  • calculate_pcc()
  • calculate_wi()

permetrics.evaluator module

class permetrics.evaluator.Evaluator(y_true=None, y_pred=None, **kwargs)

Bases: object

This is base class for all performance metrics

EPSILON = 1e-10

SUPPORT = {}

get_metric_by_name(metric_name=<class 'str'>, paras=None) → dict

Get single metric by name, specific parameter of metric by dictionary

Parameters:

• metric_name (str) – Select name of metric

• paras (dict) – Dictionary of hyper-parameter for that metric

Returns:

{ metric_name: value }

Return type:

result (dict)

get_metrics_by_dict(metrics_dict: dict) → dict

Get results of list metrics by its name and parameters wrapped by dictionary

Parameters:

metrics_dict (dict) – key is metric name and value is dict of parameters

Returns:

e.g, { “RMSE”: 0.3524, “MAE”: 0.445263 }

Return type:

dict

Examples

>>> evaluator.get_metrics_by_dict({
...     "RMSE": {"multi_output": "raw_values"},
...     "MAE": {"multi_output": "raw_values"}
... })
{"RMSE": 0.3524, "MAE": 0.445263}

get_metrics_by_list_names(list_metric_names=<class 'list'>, list_paras=None) → dict

Get results of list metrics by its name and parameters

Parameters:

• list_metric_names (list) – e.g, [“RMSE”, “MAE”, “MAPE”]

• list_paras (list) – e.g, [ {“multi_output”: “raw_values”}, {“multi_output”: “raw_values”}, {“multi_output”: [2, 3]} ]

Returns:

e.g, { “RMSE”: 0.25, “MAE”: [0.3, 0.6], “MAPE”: 0.15 }

Return type:

results (dict)

get_output_result(result=None, n_out=None, multi_output=None, force_finite=None, finite_value=None)

Get final output result based on selected parameter

Parameters:

• result – The raw result from metric

• n_out – The number of column in y_true or y_pred

• multi_output – raw_values - return multi-output, weights - return single output based on weights, else - return mean result

• force_finite – Make result as finite number

• finite_value – The value that used to replace the infinite value or NaN value.

Returns:

Final output results based on selected parameter

Return type:

final_result

get_processed_data(y_true=None, y_pred=None)

set_keyword_arguments(kwargs)

permetrics.regression module

class permetrics.regression.RegressionMetric(y_true=None, y_pred=None, **kwargs)

Bases: Evaluator

Defines a RegressionMetric class that hold all regression metrics (for both regression and time-series problems)

• An extension of scikit-learn metrics section, with the addition of many more regression metrics.

• https://scikit-learn.org/stable/modules/model_evaluation.html#classification-metrics

• Some methods in scikit-learn can’t generate the multi-output metrics, we re-implement all of them and allow multi-output metrics

• Therefore, we support calculate the multi-output metrics for all methods

Parameters:

• y_true (tuple, list, np.ndarray, default = None) – The ground truth values.

• y_pred (tuple, list, np.ndarray, default = None) – The prediction values.

A10(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

A10 index (A10)

Notes

• a10-index is engineering index for evaluating artificial intelligence models by showing the number of samples

• that fit the prediction values with a deviation of ±10% compared to experimental values

• https://www.mdpi.com/2076-3417/9/18/3715/htm

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

A10 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

A20(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

A20 index (A20)

Notes

• a20-index evaluated metric by showing the number of samples that fit the prediction values with a deviation of ±20% compared to experimental values

• https://www.mdpi.com/2076-3417/9/18/3715/htm

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

A20 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

A30(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

A30 index (A30)

Note: a30-index evaluated metric by showing the number of samples that fit the prediction values with a deviation of ±30% compared to experimental values

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

A30 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

ACOD(y_true=None, y_pred=None, X_shape=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Adjusted Coefficient of Determination (ACOD/AR2)

Notes

• https://dziganto.github.io/data%20science/linear%20regression/machine%20learning/python/Linear-Regression-101-Metrics/

• Scikit-learn and other websites denoted COD as R^2 (or R squared), it leads to the misunderstanding of R^2 in which R is PCC.

• We should denote it as COD or R2 only.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• X_shape (tuple, list, np.ndarray) – The shape of X_train dataset

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

AR2 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

AE(y_true=None, y_pred=None, **kwargs)

Absolute Error (AE) Note: Computes the absolute error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

AE metric

Return type:

result (np.ndarray)

APCC(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Absolute Pearson’s Correlation Coefficient (APCC or AR)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

AR metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

AR(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Absolute Pearson’s Correlation Coefficient (APCC or AR)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

AR metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

AR2(y_true=None, y_pred=None, X_shape=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Adjusted Coefficient of Determination (ACOD/AR2)

Notes

• https://dziganto.github.io/data%20science/linear%20regression/machine%20learning/python/Linear-Regression-101-Metrics/

• Scikit-learn and other websites denoted COD as R^2 (or R squared), it leads to the misunderstanding of R^2 in which R is PCC.

• We should denote it as COD or R2 only.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• X_shape (tuple, list, np.ndarray) – The shape of X_train dataset

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

AR2 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

CE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Cross Entropy (CE)

Notes

• Greater value of Entropy, the greater the uncertainty for probability distribution and smaller the value the less the uncertainty

• https://datascience.stackexchange.com/questions/20296/cross-entropy-loss-explanation

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

CE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

CI(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Confidence Index (or Performance Index): CI (PI)

Notes

• Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods

• > 0.85, Excellent

• 0.76-0.85, Very good

• 0.66-0.75, Good

• 0.61-0.65, Satisfactory

• 0.51-0.60, Poor

• 0.41-0.50, Bad

• < 0.40, Very bad

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

CI (PI) metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

COD(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Coefficient of Determination (COD/R2)

Notes

• https://scikit-learn.org/stable/modules/model_evaluation.html#r2-score

• Scikit-learn and other websites denoted COD as R^2 (or R squared), it leads to the misunderstanding of R^2 in which R is PCC.

• We should denote it as COD or R2 only.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R2 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

COR(y_true=None, y_pred=None, sample=False, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Correlation (COR) Links: https://corporatefinanceinstitute.com/resources/data-science/covariance/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• sample (bool) – sample covariance or population covariance. See the website above for more details

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

COR metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

COV(y_true=None, y_pred=None, sample=False, multi_output='raw_values', force_finite=True, finite_value=-10.0, **kwargs)

Covariance (COV)

• is a measure of the relationship between two random variables

• evaluates how much – to what extent – the variables change together

• does not assess the dependency between variables

• Positive covariance: Indicates that two variables tend to move in the same direction.

• Negative covariance: Reveals that two variables tend to move in inverse directions.

Links:

• https://corporatefinanceinstitute.com/resources/data-science/covariance/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• sample (bool) – sample covariance or population covariance. See the website above for more details

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

COV metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

CRM(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Coefficient of Residual Mass (CRM) Links: https://doi.org/10.1016/j.csite.2022.101797

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

CRM metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

DRV(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=10.0, **kwargs)

Deviation of Runoff Volume (DRV) Link: https://rstudio-pubs-static.s3.amazonaws.com/433152_56d00c1e29724829bad5fc4fd8c8ebff.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

DRV metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

EC(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Efficiency Coefficient (EC) Links: https://doi.org/10.1016/j.solener.2019.01.037

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

EC metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

EVS(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Explained Variance Score (EVS)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

EVS metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

JSD(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Jensen-Shannon Divergence (JSD) Link: https://machinelearningmastery.com/divergence-between-probability-distributions/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

JSD metric (bits) for single column or multiple columns

Return type:

result (float, int, np.ndarray)

KGE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Kling-Gupta Efficiency (KGE) Link: https://rstudio-pubs-static.s3.amazonaws.com/433152_56d00c1e29724829bad5fc4fd8c8ebff.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

KGE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

KLD(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Kullback-Leibler Divergence (KLD) Link: https://machinelearningmastery.com/divergence-between-probability-distributions/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

KLD metric (bits) for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MAAPE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Arctangent Absolute Percentage Error (MAAPE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MAAPE metric for single column or multiple columns (radian values)

Return type:

result (float, int, np.ndarray)

MAE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Absolute Error (MAE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MAE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MAPE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Absolute Percentage Error (MAPE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MAPE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MASE(y_true=None, y_pred=None, m=1, multi_output='raw_values', force_finite=True, finite_value=10000000000.0, **kwargs)

Mean Absolute Scaled Error (MASE) Link: https://en.wikipedia.org/wiki/Mean_absolute_scaled_error

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• m (int) – m = 1 for non-seasonal data, m > 1 for seasonal data. (Optional, default = 1)

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 1e10)

Returns:

MASE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MBE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Bias Error (MBE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MBE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

ME(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Max Error (ME)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

ME metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MPE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Percentage Error (MPE) Link: https://www.dataquest.io/blog/understanding-regression-error-metrics/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MPE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MRB(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Relative Error (MRE) - Mean Relative Bias (MRB)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MRE (MRB) metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MRE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Relative Error (MRE) - Mean Relative Bias (MRB)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MRE (MRB) metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MSE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Squared Error (MSE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MSLE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Squared Log Error (MSLE) Link: https://peltarion.com/knowledge-center/documentation/modeling-view/build-an-ai-model/loss-functions/mean-squared-logarithmic-error-(msle)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MSLE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

MedAE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Median Absolute Error (MedAE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MedAE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

NGINI(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Normalized Gini Coefficient for Regression (Actuarial Lorenz / Ranking Power). Measures how well the predictions rank the actual continuous targets. Best possible score is 1.0 (perfect ranking), 0.0 is random ranking. Range = [-1, 1].

References

• Frees, Edward W., Glenn Meyers, and A. David Cummings. “Summarizing insurance scores using a Gini index.” Journal of the American Statistical Association 106.495 (2011): 1085-1098.

NNSE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Normalize Nash-Sutcliffe Efficiency (NNSE) Link: https://agrimetsoft.com/calculators/Nash%20Sutcliffe%20model%20Efficiency%20coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

NSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

NRMSE(y_true=None, y_pred=None, normalization='mean', multi_output='raw_values', force_finite=True, finite_value=10000000000.0, **kwargs)

Normalized Root Mean Square Error (NRMSE).

References

• https://www.marinedatascience.co/blog/2019/01/07/normalizing-the-rmse/

• https://en.wikipedia.org/wiki/Root-mean-square_deviation#Normalized_root-mean-square_deviation

• https://search.r-project.org/CRAN/refmans/hydroGOF/html/nrmse.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• normalization (str) – The method to normalize RMSE. Valid values: - “mean”: Normalizes by the mean of y_true (also known as CV(RMSE)). - “range”: Normalizes by the difference between max and min of y_true. - “std”: Normalizes by the standard deviation of y_true. - “iqr”: Normalizes by the Interquartile Range (Q3 - Q1) of y_true.

• multi_output – Can be “raw_values” or list weights of variables.

• force_finite (bool) – Replace NaN or Inf results with finite_value.

• finite_value (float) – Replacement value for Non-finite errors.

NSE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Nash-Sutcliffe Efficiency (NSE) Link: https://agrimetsoft.com/calculators/Nash%20Sutcliffe%20model%20Efficiency%20coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

NSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

OI(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Overall Index (OI) Links: https://doi.org/10.1016/j.solener.2019.01.037

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

OI metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

PCC(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Pearson’s Correlation Coefficient (PCC or R) .. rubric:: Notes

• Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods

• Remember no absolute in the equations

• https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

PCD(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Prediction of Change in Direction (PCD)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

PCD metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

R(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Pearson’s Correlation Coefficient (PCC or R) .. rubric:: Notes

• Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods

• Remember no absolute in the equations

• https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

R2(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Coefficient of Determination (COD/R2)

Notes

• https://scikit-learn.org/stable/modules/model_evaluation.html#r2-score

• Scikit-learn and other websites denoted COD as R^2 (or R squared), it leads to the misunderstanding of R^2 in which R is PCC.

• We should denote it as COD or R2 only.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R2 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

R2S(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

(Pearson’s Correlation Index)^2 = R^2 = R2S = RSQ (R square)

Notes

• Do not misunderstand between R2s and R2 (Coefficient of Determination), they are different

• Most of online tutorials (article, wikipedia,…) or even scikit-learn library are denoted the wrong R2s and R2.

• R^2 = R2s = R squared should be (Pearson’s Correlation Index)^2

• Meanwhile, R2 = Coefficient of Determination

• https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R2s metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

RAE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=10000000000.0, **kwargs)

Relative Absolute Error (RAE)

Notes

• WEKA Standard: https://waikato.github.io/weka-wiki/formats_and_processing/evaluating_models/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RAE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

RB(y_true=None, y_pred=None, **kwargs)

Relative Error (RE) Note: Computes the relative error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

RE metric

Return type:

result (np.ndarray)

RE(y_true=None, y_pred=None, **kwargs)

Relative Error (RE) Note: Computes the relative error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

RE metric

Return type:

result (np.ndarray)

RGINI(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Gini Index of Absolute Residuals (Error Dispersion).

References

• Yitzhaki, Shlomo, and Edna Schechtman. The Gini methodology: a primer on a statistical methodology. Vol. 272. Springer Science & Business Media, 2012.

RMSE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Root Mean Squared Error (RMSE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RMSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

RRSE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Root Relative Squared Error (RRSE)

Notes

• WEKA Standard: https://waikato.github.io/weka-wiki/formats_and_processing/evaluating_models/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RRSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

RSE(y_true=None, y_pred=None, X_shape=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Residual Standard Error (RSE)

Links:

• https://www.statology.org/residual-standard-error-r/

• https://machinelearningmastery.com/degrees-of-freedom-in-machine-learning/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• X_shape (tuple, list, np.ndarray) – The shape of X_train dataset

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

RSQ(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

(Pearson’s Correlation Index)^2 = R^2 = R2S = RSQ (R square)

Notes

• Do not misunderstand between R2s and R2 (Coefficient of Determination), they are different

• Most of online tutorials (article, wikipedia,…) or even scikit-learn library are denoted the wrong R2s and R2.

• R^2 = R2s = R squared should be (Pearson’s Correlation Index)^2

• Meanwhile, R2 = Coefficient of Determination

• https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R2s metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

SE(y_true=None, y_pred=None, **kwargs)

Squared Error (SE) Note: Computes the squared error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

SE metric

Return type:

result (np.ndarray)

SLE(y_true=None, y_pred=None, **kwargs)

Squared Log Error (SLE) Note: Computes the squared log error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

SLE metric

Return type:

result (np.ndarray)

SMAPE(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=200.0, **kwargs)

Symmetric Mean Absolute Percentage Error (SMAPE). Original version. Range [0, 200%]. References: Forecasting, Long-Range. “From Crystal Ball to Computer.” Scott Armstrong Robert J. Genetski (1978).

SMAPE_NP(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=2.0, **kwargs)

Symmetric Mean Absolute Percentage Error (SMAPE_NP) Original version. Range [0, 2]. References: Forecasting, Long-Range. “From Crystal Ball to Computer.” Scott Armstrong Robert J. Genetski (1978).

SMAPE_S(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Symmetric Mean Absolute Percentage Error Simplified (SMAPE_S). Simplified version of SMAPE with Range [0, 1] (or [0, 100%]), smaller is better. References: Makridakis, Spyros. “Accuracy measures: theoretical and practical concerns.” International journal of forecasting 9.4 (1993): 527-529.

SMAPE_S_P(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=100.0, **kwargs)

Symmetric Mean Absolute Percentage Error Simplified (SMAPE_S_P). Simplified version of SMAPE with Range [0, 1] (or [0, 100%]), smaller is better. References: Makridakis, Spyros. “Accuracy measures: theoretical and practical concerns.” International journal of forecasting 9.4 (1993): 527-529.

SUPPORT = {'A10': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'A20': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'A30': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'ACOD': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'AE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'APCC': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'AR': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'AR2': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'CE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'CI': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'COD': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'COR': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'COV': {'best': 'unknown', 'range': '(-inf, +inf)', 'type': 'max'}, 'CRM': {'best': '0', 'range': '(-inf, +inf)', 'type': 'min'}, 'DRV': {'best': '1', 'range': '(-inf, +inf)', 'type': 'unknown'}, 'EC': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'EVS': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'JSD': {'best': '0', 'range': '[0, 1]', 'type': 'min'}, 'KGE': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'KLD': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MAAPE': {'best': '0', 'range': '[0, +1.5708)', 'type': 'min'}, 'MAE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MAPE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MASE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MBE': {'best': '0', 'range': '(-inf, +inf)', 'type': 'unknown'}, 'ME': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MPE': {'best': '0', 'range': '(-inf, +inf)', 'type': 'unknown'}, 'MRB': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MRE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MSE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MSLE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'MedAE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'NGINI': {'best': '1', 'range': '[-1, +1]', 'type': 'max'}, 'NNSE': {'best': '1', 'range': '(0, 1]', 'type': 'max'}, 'NRMSE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'NSE': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'OI': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'PCC': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'PCD': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'R': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'R2': {'best': '1', 'range': '(-inf, 1]', 'type': 'max'}, 'R2S': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'RAE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'RB': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'RE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'RGINI': {'best': '0', 'range': '[0, +1]', 'type': 'min'}, 'RMSE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'RRSE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'RSE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'RSQ': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'SE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'SLE': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'SMAPE': {'best': '0', 'range': '[0, 200]', 'type': 'min'}, 'SMAPE_NP': {'best': '0', 'range': '[0, 2]', 'type': 'min'}, 'SMAPE_S': {'best': '0', 'range': '[0, 1]', 'type': 'min'}, 'SMAPE_S_P': {'best': '0', 'range': '[0, 100]', 'type': 'min'}, 'VAF': {'best': '100', 'range': '(-inf, 100)', 'type': 'max'}, 'WI': {'best': '1', 'range': '[0, 1]', 'type': 'max'}}

VAF(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Variance Accounted For between 2 signals (VAF) Link: https://www.dcsc.tudelft.nl/~jwvanwingerden/lti/doc/html/vaf.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

VAF metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

WI(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Willmott Index (WI)

Notes

• Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods

• https://www.researchgate.net/publication/319699360_Reference_evapotranspiration_for_Londrina_Parana_Brazil_performance_of_different_estimation_methods

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

WI metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

a10_index(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

A10 index (A10)

Notes

• a10-index is engineering index for evaluating artificial intelligence models by showing the number of samples

• that fit the prediction values with a deviation of ±10% compared to experimental values

• https://www.mdpi.com/2076-3417/9/18/3715/htm

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

A10 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

a20_index(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

A20 index (A20)

Notes

• a20-index evaluated metric by showing the number of samples that fit the prediction values with a deviation of ±20% compared to experimental values

• https://www.mdpi.com/2076-3417/9/18/3715/htm

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

A20 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

a30_index(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

A30 index (A30)

Note: a30-index evaluated metric by showing the number of samples that fit the prediction values with a deviation of ±30% compared to experimental values

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

A30 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

absolute_pearson_correlation_coefficient(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Absolute Pearson’s Correlation Coefficient (APCC or AR)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

AR metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

adjusted_coefficient_of_determination(y_true=None, y_pred=None, X_shape=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Adjusted Coefficient of Determination (ACOD/AR2)

Notes

• https://dziganto.github.io/data%20science/linear%20regression/machine%20learning/python/Linear-Regression-101-Metrics/

• Scikit-learn and other websites denoted COD as R^2 (or R squared), it leads to the misunderstanding of R^2 in which R is PCC.

• We should denote it as COD or R2 only.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• X_shape (tuple, list, np.ndarray) – The shape of X_train dataset

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

AR2 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

coefficient_of_determination(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Coefficient of Determination (COD/R2)

Notes

• https://scikit-learn.org/stable/modules/model_evaluation.html#r2-score

• Scikit-learn and other websites denoted COD as R^2 (or R squared), it leads to the misunderstanding of R^2 in which R is PCC.

• We should denote it as COD or R2 only.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R2 metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

coefficient_of_residual_mass(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Coefficient of Residual Mass (CRM) Links: https://doi.org/10.1016/j.csite.2022.101797

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

CRM metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

confidence_index(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Confidence Index (or Performance Index): CI (PI)

Notes

• Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods

• > 0.85, Excellent

• 0.76-0.85, Very good

• 0.66-0.75, Good

• 0.61-0.65, Satisfactory

• 0.51-0.60, Poor

• 0.41-0.50, Bad

• < 0.40, Very bad

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

CI (PI) metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

correlation(y_true=None, y_pred=None, sample=False, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Correlation (COR) Links: https://corporatefinanceinstitute.com/resources/data-science/covariance/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• sample (bool) – sample covariance or population covariance. See the website above for more details

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

COR metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

covariance(y_true=None, y_pred=None, sample=False, multi_output='raw_values', force_finite=True, finite_value=-10.0, **kwargs)

Covariance (COV)

• is a measure of the relationship between two random variables

• evaluates how much – to what extent – the variables change together

• does not assess the dependency between variables

• Positive covariance: Indicates that two variables tend to move in the same direction.

• Negative covariance: Reveals that two variables tend to move in inverse directions.

Links:

• https://corporatefinanceinstitute.com/resources/data-science/covariance/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• sample (bool) – sample covariance or population covariance. See the website above for more details

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

COV metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

cross_entropy(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Cross Entropy (CE)

Notes

• Greater value of Entropy, the greater the uncertainty for probability distribution and smaller the value the less the uncertainty

• https://datascience.stackexchange.com/questions/20296/cross-entropy-loss-explanation

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

CE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

deviation_of_runoff_volume(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=10.0, **kwargs)

Deviation of Runoff Volume (DRV) Link: https://rstudio-pubs-static.s3.amazonaws.com/433152_56d00c1e29724829bad5fc4fd8c8ebff.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

DRV metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

efficiency_coefficient(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Efficiency Coefficient (EC) Links: https://doi.org/10.1016/j.solener.2019.01.037

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

EC metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

explained_variance_score(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Explained Variance Score (EVS)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

EVS metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

get_processed_data(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

y_true used in evaluation process. y_pred_final: y_pred used in evaluation process n_out: Number of outputs

Return type:

y_true_final

static get_support(name=None, verbose=True)

jensen_shannon_divergence(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Jensen-Shannon Divergence (JSD) Link: https://machinelearningmastery.com/divergence-between-probability-distributions/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

JSD metric (bits) for single column or multiple columns

Return type:

result (float, int, np.ndarray)

kling_gupta_efficiency(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Kling-Gupta Efficiency (KGE) Link: https://rstudio-pubs-static.s3.amazonaws.com/433152_56d00c1e29724829bad5fc4fd8c8ebff.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

KGE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

kullback_leibler_divergence(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Kullback-Leibler Divergence (KLD) Link: https://machinelearningmastery.com/divergence-between-probability-distributions/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

KLD metric (bits) for single column or multiple columns

Return type:

result (float, int, np.ndarray)

max_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Max Error (ME)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

ME metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_absolute_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Absolute Error (MAE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MAE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_absolute_percentage_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Absolute Percentage Error (MAPE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MAPE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_absolute_scaled_error(y_true=None, y_pred=None, m=1, multi_output='raw_values', force_finite=True, finite_value=10000000000.0, **kwargs)

Mean Absolute Scaled Error (MASE) Link: https://en.wikipedia.org/wiki/Mean_absolute_scaled_error

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• m (int) – m = 1 for non-seasonal data, m > 1 for seasonal data. (Optional, default = 1)

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 1e10)

Returns:

MASE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_arctangent_absolute_percentage_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Arctangent Absolute Percentage Error (MAAPE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MAAPE metric for single column or multiple columns (radian values)

Return type:

result (float, int, np.ndarray)

mean_bias_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Bias Error (MBE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MBE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_percentage_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Percentage Error (MPE) Link: https://www.dataquest.io/blog/understanding-regression-error-metrics/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MPE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_relative_bias(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Relative Error (MRE) - Mean Relative Bias (MRB)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MRE (MRB) metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_relative_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Relative Error (MRE) - Mean Relative Bias (MRB)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MRE (MRB) metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_squared_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Squared Error (MSE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

mean_squared_log_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Mean Squared Log Error (MSLE) Link: https://peltarion.com/knowledge-center/documentation/modeling-view/build-an-ai-model/loss-functions/mean-squared-logarithmic-error-(msle)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MSLE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

median_absolute_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Median Absolute Error (MedAE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

MedAE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

nash_sutcliffe_efficiency(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Nash-Sutcliffe Efficiency (NSE) Link: https://agrimetsoft.com/calculators/Nash%20Sutcliffe%20model%20Efficiency%20coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

NSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

normalized_gini_coefficient(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Normalized Gini Coefficient for Regression (Actuarial Lorenz / Ranking Power). Measures how well the predictions rank the actual continuous targets. Best possible score is 1.0 (perfect ranking), 0.0 is random ranking. Range = [-1, 1].

References

• Frees, Edward W., Glenn Meyers, and A. David Cummings. “Summarizing insurance scores using a Gini index.” Journal of the American Statistical Association 106.495 (2011): 1085-1098.

normalized_nash_sutcliffe_efficiency(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Normalize Nash-Sutcliffe Efficiency (NNSE) Link: https://agrimetsoft.com/calculators/Nash%20Sutcliffe%20model%20Efficiency%20coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

NSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

normalized_root_mean_square_error(y_true=None, y_pred=None, normalization='mean', multi_output='raw_values', force_finite=True, finite_value=10000000000.0, **kwargs)

Normalized Root Mean Square Error (NRMSE).

References

• https://www.marinedatascience.co/blog/2019/01/07/normalizing-the-rmse/

• https://en.wikipedia.org/wiki/Root-mean-square_deviation#Normalized_root-mean-square_deviation

• https://search.r-project.org/CRAN/refmans/hydroGOF/html/nrmse.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• normalization (str) – The method to normalize RMSE. Valid values: - “mean”: Normalizes by the mean of y_true (also known as CV(RMSE)). - “range”: Normalizes by the difference between max and min of y_true. - “std”: Normalizes by the standard deviation of y_true. - “iqr”: Normalizes by the Interquartile Range (Q3 - Q1) of y_true.

• multi_output – Can be “raw_values” or list weights of variables.

• force_finite (bool) – Replace NaN or Inf results with finite_value.

• finite_value (float) – Replacement value for Non-finite errors.

overall_index(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Overall Index (OI) Links: https://doi.org/10.1016/j.solener.2019.01.037

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

OI metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

pearson_correlation_coefficient(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=-1.0, **kwargs)

Pearson’s Correlation Coefficient (PCC or R) .. rubric:: Notes

• Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods

• Remember no absolute in the equations

• https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

pearson_correlation_coefficient_square(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

(Pearson’s Correlation Index)^2 = R^2 = R2S = RSQ (R square)

Notes

• Do not misunderstand between R2s and R2 (Coefficient of Determination), they are different

• Most of online tutorials (article, wikipedia,…) or even scikit-learn library are denoted the wrong R2s and R2.

• R^2 = R2s = R squared should be (Pearson’s Correlation Index)^2

• Meanwhile, R2 = Coefficient of Determination

• https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

R2s metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

prediction_of_change_in_direction(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Prediction of Change in Direction (PCD)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

PCD metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

relative_absolute_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=10000000000.0, **kwargs)

Relative Absolute Error (RAE)

Notes

• WEKA Standard: https://waikato.github.io/weka-wiki/formats_and_processing/evaluating_models/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RAE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

residual_gini_index(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Gini Index of Absolute Residuals (Error Dispersion).

References

• Yitzhaki, Shlomo, and Edna Schechtman. The Gini methodology: a primer on a statistical methodology. Vol. 272. Springer Science & Business Media, 2012.

residual_standard_error(y_true=None, y_pred=None, X_shape=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Residual Standard Error (RSE)

Links:

• https://www.statology.org/residual-standard-error-r/

• https://machinelearningmastery.com/degrees-of-freedom-in-machine-learning/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• X_shape (tuple, list, np.ndarray) – The shape of X_train dataset

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

root_mean_squared_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Root Mean Squared Error (RMSE)

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RMSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

root_relative_squared_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Root Relative Squared Error (RRSE)

Notes

• WEKA Standard: https://waikato.github.io/weka-wiki/formats_and_processing/evaluating_models/

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

RRSE metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

single_absolute_error(y_true=None, y_pred=None, **kwargs)

Absolute Error (AE) Note: Computes the absolute error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

AE metric

Return type:

result (np.ndarray)

single_relative_bias(y_true=None, y_pred=None, **kwargs)

Relative Error (RE) Note: Computes the relative error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

RE metric

Return type:

result (np.ndarray)

single_relative_error(y_true=None, y_pred=None, **kwargs)

Relative Error (RE) Note: Computes the relative error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

RE metric

Return type:

result (np.ndarray)

single_squared_error(y_true=None, y_pred=None, **kwargs)

Squared Error (SE) Note: Computes the squared error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

SE metric

Return type:

result (np.ndarray)

single_squared_log_error(y_true=None, y_pred=None, **kwargs)

Squared Log Error (SLE) Note: Computes the squared log error between two numbers, or for element between a pair of list, tuple or numpy arrays.

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

Returns:

SLE metric

Return type:

result (np.ndarray)

symmetric_mean_absolute_percentage_error(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=200.0, **kwargs)

Symmetric Mean Absolute Percentage Error (SMAPE). Original version. Range [0, 200%]. References: Forecasting, Long-Range. “From Crystal Ball to Computer.” Scott Armstrong Robert J. Genetski (1978).

symmetric_mean_absolute_percentage_error_np(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=2.0, **kwargs)

Symmetric Mean Absolute Percentage Error (SMAPE_NP) Original version. Range [0, 2]. References: Forecasting, Long-Range. “From Crystal Ball to Computer.” Scott Armstrong Robert J. Genetski (1978).

symmetric_mean_absolute_percentage_error_simplified(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=1.0, **kwargs)

Symmetric Mean Absolute Percentage Error Simplified (SMAPE_S). Simplified version of SMAPE with Range [0, 1] (or [0, 100%]), smaller is better. References: Makridakis, Spyros. “Accuracy measures: theoretical and practical concerns.” International journal of forecasting 9.4 (1993): 527-529.

symmetric_mean_absolute_percentage_error_simplified_p(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=100.0, **kwargs)

Symmetric Mean Absolute Percentage Error Simplified (SMAPE_S_P). Simplified version of SMAPE with Range [0, 1] (or [0, 100%]), smaller is better. References: Makridakis, Spyros. “Accuracy measures: theoretical and practical concerns.” International journal of forecasting 9.4 (1993): 527-529.

variance_accounted_for(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Variance Accounted For between 2 signals (VAF) Link: https://www.dcsc.tudelft.nl/~jwvanwingerden/lti/doc/html/vaf.html

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

VAF metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

willmott_index(y_true=None, y_pred=None, multi_output='raw_values', force_finite=True, finite_value=0.0, **kwargs)

Willmott Index (WI)

Notes

• Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods

• https://www.researchgate.net/publication/319699360_Reference_evapotranspiration_for_Londrina_Parana_Brazil_performance_of_different_estimation_methods

Parameters:

• y_true (tuple, list, np.ndarray) – The ground truth values

• y_pred (tuple, list, np.ndarray) – The prediction values

• multi_output – Can be “raw_values” or list weights of variables such as [0.5, 0.2, 0.3] for 3 columns, (Optional, default = “raw_values”)

• force_finite (bool) – When result is not finite, it can be NaN or Inf. Their result will be replaced by finite_value (Optional, default = True)

• finite_value (float) – The finite value used to replace Inf or NaN result (Optional, default = 0.0)

Returns:

WI metric for single column or multiple columns

Return type:

result (float, int, np.ndarray)

permetrics.classification module

class permetrics.classification.ClassificationMetric(y_true=None, y_pred=None, **kwargs)

Bases: Evaluator

A class for evaluating classification metrics.

Parameters:

• y_true (tuple, list, np.ndarray, optional) – The ground truth values. Default is None.

• y_pred (tuple, list, np.ndarray, optional) – The predicted values. Default is None.

• labels (tuple, list, np.ndarray, optional) – List of labels to index the matrix. This may be used to reorder or select a subset of labels. Default is None.

• pos_label (int or str) – Positive label for binary classification.

• average (str or None, optional) – Determines the type of averaging performed on the data. Options are: - ‘binary’: Calculate for binary classification problem - ‘micro’: Calculate metrics globally by considering each element of the label indicator matrix as a label. - ‘macro’: Calculate metrics for each label and find their unweighted mean. - ‘weighted’: Calculate metrics for each label and find their average, weighted by support. - None: Scores for each class are returned. Default is “binary”.

get_support(name=None, verbose=True)

Retrieve the support information for a specific metric or all metrics.

get_processed_data(y_true=None, y_pred=None)

Process and format the input data for evaluation.

get_processed_data2(y_true=None, y_pred=None)

Process and format the input data for ROC and probability-based metrics.

precision_score(...)

Calculate the precision score.

negative_predictive_value(...)

Calculate the negative predictive value.

specificity_score(...)

Calculate the specificity score.

recall_score(...)

Calculate the recall score.

f1_score(...)

Calculate the F1 score.

f2_score(...)

Calculate the F2 score.

fbeta_score(...)

Calculate the F-beta score.

matthews_correlation_coefficient(...)

Calculate the Matthews correlation coefficient.

hamming_loss(...)

Calculate the hamming loss.

lift_score(...)

Calculate the lift score.

cohen_kappa_score(...)

Calculate the Cohen’s kappa score.

jaccard_similarity_index(...)

Calculate the Jaccard similarity index.

g_mean_score(...)

Calculate the geometric mean score.

accuracy_score(...)

Calculate the accuracy score.

confusion_matrix(...)

Generate the confusion matrix.

roc_auc_score(...)

Calculate the ROC-AUC score.

gini_index(...)

Calculate the Gini index.

brier_score_loss(...)

Calculate the Brier score loss.

crossentropy_loss(...)

Calculate the cross-entropy loss.

hinge_loss(...)

Calculate the hinge loss.

kullback_leibler_divergence_loss(...)

Calculate the Kullback-Leibler divergence loss.

AS(y_true=None, y_pred=None, normalize=True, sample_weight=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated target values.

• normalize (bool, optional) – If True, return the fraction of correctly classified samples (float). If False, return the number of correctly classified samples (int).

• sample_weight (array-like, optional) – Sample weights.

Returns:

Accuracy score.

Return type:

float or int

AUC(y_true=None, y_pred=None, average='macro', **kwargs)

Compute the Area Under the Receiver Operating Characteristic Curve (ROC AUC).

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated probabilities or decision function.

• average (str, optional) – Averaging method (‘macro’, ‘weighted’, or None).

Returns:

ROC AUC score.

Return type:

float or dict

BSL(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted probabilities.

Returns:

Brier score loss.

Return type:

float

CEL(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted probabilities.

Returns:

Cross-entropy loss.

Return type:

float

CKS(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Cohen’s kappa score.

Return type:

float or dict

CM(y_true=None, y_pred=None, labels=None, normalize=None, **kwargs)

Compute the confusion matrix for classification tasks.

Parameters:

• y_true (array-like) – Ground truth (correct) labels.

• y_pred (array-like) – Predicted labels.

• labels (list, optional) – Subset of labels to include in the matrix. Default is None.

• normalize (str, optional) – Normalization method. One of {“true”, “pred”, “all”}. - “true”: Normalize rows (true labels). - “pred”: Normalize columns (predicted labels). - “all”: Normalize the entire matrix. Default is None (no normalization).

Returns:

• matrix (ndarray): Confusion matrix (normalized if specified).

• imap (dict): Mapping of labels to matrix indices.

• imap_count (dict): Count of true labels for each class.

Return type:

tuple

Raises:

ValueError – If specified labels do not exist in y_true or y_pred.

F1S(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

F1 score.

Return type:

float or dict

F2S(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

F2 score.

Return type:

float or dict

FBS(y_true=None, y_pred=None, beta=1.0, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• beta (float, optional) – Weight of recall in the F-beta score.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

F-beta score.

Return type:

float or dict

GINI(y_true=None, y_pred=None, **kwargs)

Compute the Gini index based on the ROC AUC score.

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated probabilities or decision function.

Returns:

Gini index.

Return type:

float or dict

GMS(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Geometric mean (G-mean) score.

Return type:

float or dict

HGL(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted scores.

Returns:

Hinge loss.

Return type:

float

HML(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Hamming loss.

Return type:

float or dict

JSC(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Jaccard similarity index.

Return type:

float or dict

JSI(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Jaccard similarity index.

Return type:

float or dict

JSS(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Jaccard similarity index.

Return type:

float or dict

KLDL(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted probabilities.

Returns:

Kullback-Leibler divergence loss.

Return type:

float

LS(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Lift score.

Return type:

float or dict

MCC(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Matthews correlation coefficient.

Return type:

float or dict

NPV(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Calculate the negative predictive value.

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Negative predictive value.

Return type:

float or dict

PS(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Precision score.

Return type:

float or dict

RAS(y_true=None, y_pred=None, average='macro', **kwargs)

Compute the Area Under the Receiver Operating Characteristic Curve (ROC AUC).

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated probabilities or decision function.

• average (str, optional) – Averaging method (‘macro’, ‘weighted’, or None).

Returns:

ROC AUC score.

Return type:

float or dict

ROC(y_true=None, y_pred=None, average='macro', **kwargs)

Compute the Area Under the Receiver Operating Characteristic Curve (ROC AUC).

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated probabilities or decision function.

• average (str, optional) – Averaging method (‘macro’, ‘weighted’, or None).

Returns:

ROC AUC score.

Return type:

float or dict

RS(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Recall score.

Return type:

float or dict

SS(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Calculate the specificity score.

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Specificity score.

Return type:

float or dict

SUPPORT = {'AS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'AUC': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'BSL': {'best': '0', 'range': '[0, 1]', 'type': 'min'}, 'CEL': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'CKS': {'best': '1', 'range': '[-1, +1]', 'type': 'max'}, 'F1S': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'F2S': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'FBS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'GINI': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'GMS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'HGL': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'HML': {'best': '0', 'range': '[0, 1]', 'type': 'min'}, 'JSI': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'JSS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'KLDL': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'LS': {'best': 'unknown', 'range': '[0, +inf)', 'type': 'max'}, 'MCC': {'best': '1', 'range': '[-1, +1]', 'type': 'max'}, 'NPV': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'PS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'ROC': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'ROC-AUC': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'RS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'SS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}}

accuracy_score(y_true=None, y_pred=None, normalize=True, sample_weight=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated target values.

• normalize (bool, optional) – If True, return the fraction of correctly classified samples (float). If False, return the number of correctly classified samples (int).

• sample_weight (array-like, optional) – Sample weights.

Returns:

Accuracy score.

Return type:

float or int

brier_score_loss(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted probabilities.

Returns:

Brier score loss.

Return type:

float

cohen_kappa_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Cohen’s kappa score.

Return type:

float or dict

confusion_matrix(y_true=None, y_pred=None, labels=None, normalize=None, **kwargs)

Compute the confusion matrix for classification tasks.

Parameters:

• y_true (array-like) – Ground truth (correct) labels.

• y_pred (array-like) – Predicted labels.

• labels (list, optional) – Subset of labels to include in the matrix. Default is None.

• normalize (str, optional) – Normalization method. One of {“true”, “pred”, “all”}. - “true”: Normalize rows (true labels). - “pred”: Normalize columns (predicted labels). - “all”: Normalize the entire matrix. Default is None (no normalization).

Returns:

• matrix (ndarray): Confusion matrix (normalized if specified).

• imap (dict): Mapping of labels to matrix indices.

• imap_count (dict): Count of true labels for each class.

Return type:

tuple

Raises:

ValueError – If specified labels do not exist in y_true or y_pred.

crossentropy_loss(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted probabilities.

Returns:

Cross-entropy loss.

Return type:

float

f1_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

F1 score.

Return type:

float or dict

f2_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

F2 score.

Return type:

float or dict

fbeta_score(y_true=None, y_pred=None, beta=1.0, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• beta (float, optional) – Weight of recall in the F-beta score.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

F-beta score.

Return type:

float or dict

g_mean_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Geometric mean (G-mean) score.

Return type:

float or dict

get_processed_data(y_true=None, y_pred=None)

Process and format the input data for evaluation.

Returns:

y_true used in evaluation process. y_pred_final: y_pred used in evaluation process unique_classes: All unique classes from y_true and y_pred representor: the label is number or string

Return type:

y_true_final

get_processed_data2(y_true=None, y_pred=None)

Returns:

y_true used in evaluation process. y_pred_final: y_pred used in evaluation process binary: is problem binary or multi-class classification representor: the label is number or string

Return type:

y_true_final

static get_support(name=None, verbose=True)

Retrieve the support information for a specific metric or all metrics.

Parameters:

• name (str, optional) – Name of the metric to retrieve. Use “all” to retrieve all metrics.

• verbose (bool, optional) – Whether to print the metric details.

Returns:

Support information for the specified metric(s).

Return type:

dict

gini_index(y_true=None, y_pred=None, **kwargs)

Compute the Gini index based on the ROC AUC score.

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated probabilities or decision function.

Returns:

Gini index.

Return type:

float or dict

hamming_loss(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Hamming loss.

Return type:

float or dict

hinge_loss(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted scores.

Returns:

Hinge loss.

Return type:

float

jaccard_similarity_coefficient(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Jaccard similarity index.

Return type:

float or dict

jaccard_similarity_index(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Jaccard similarity index.

Return type:

float or dict

jaccard_similarity_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Jaccard similarity index.

Return type:

float or dict

kullback_leibler_divergence_loss(y_true=None, y_pred=None, **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Predicted probabilities.

Returns:

Kullback-Leibler divergence loss.

Return type:

float

lift_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Lift score.

Return type:

float or dict

matthews_correlation_coefficient(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Matthews correlation coefficient.

Return type:

float or dict

negative_predictive_value(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Calculate the negative predictive value.

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Negative predictive value.

Return type:

float or dict

precision_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Precision score.

Return type:

float or dict

recall_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Recall score.

Return type:

float or dict

roc_auc_score(y_true=None, y_pred=None, average='macro', **kwargs)

Compute the Area Under the Receiver Operating Characteristic Curve (ROC AUC).

Parameters:

• y_true (array-like, optional) – Ground truth (correct) target values.

• y_pred (array-like, optional) – Estimated probabilities or decision function.

• average (str, optional) – Averaging method (‘macro’, ‘weighted’, or None).

Returns:

ROC AUC score.

Return type:

float or dict

specificity_score(y_true=None, y_pred=None, labels=None, pos_label=1, average='binary', **kwargs)

Calculate the specificity score.

Parameters:

• y_true (array-like, optional) – Ground truth values.

• y_pred (array-like, optional) – Predicted values.

• labels (list, optional) – List of labels to include in the calculation.

• pos_label (int or str, optional) – The positive class label for binary classification.

• average (str, optional) – Averaging method (‘binary’, ‘micro’, ‘macro’, ‘weighted’, or None).

Returns:

Specificity score.

Return type:

float or dict

permetrics.clustering module

class permetrics.clustering.ClusteringMetric(y_true=None, y_pred=None, X=None, force_finite=True, finite_value=None, **kwargs)

Bases: Evaluator

Defines a ClusteringMetric class that holds all internal and external metrics for clustering problems.

This class provides a unified interface to compute a wide range of clustering validation indexes (CVIs), including both internal metrics (requiring only data features $X$ and predicted labels) and external metrics (requiring ground truth labels).

Parameters:

• y_true (tuple, list, or np.ndarray, default=None) – The ground truth class labels. Used for calculating external validation metrics.

• y_pred (tuple, list, or np.ndarray, default=None) – The predicted cluster labels. Used for both internal and external metrics.

• X (tuple, list, or np.ndarray, default=None) – The input feature matrix/dataset of shape (n_samples, n_features). Required for internal validation metrics.

• force_finite (bool, default=True) – If True, non-finite values (such as NaN or Inf) resulting from undefined mathematical operations (e.g., division by zero) will be replaced by finite_value.

• finite_value (float, default=None) – The specific fallback value used to replace infinite or NaN results when force_finite is True.

X

Stored feature dataset.

Type:

np.ndarray or None

le

The label encoder instance used during internal data formatting.

Type:

LabelEncoder or None

force_finite

Flag indicating whether to replace non-finite metrics.

Type:

bool

finite_value

Fallback value for non-finite metrics.

Type:

float or None

ARS(y_true=None, y_pred=None, **kwargs)

Computes the Adjusted rand score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Adjusted rand score

Return type:

result (float)

BHI(X=None, y_pred=None, **kwargs)

The Ball-Hall Index (1995) is the mean of the mean dispersion across all clusters. The largest difference between successive clustering levels indicates the optimal number of clusters. Smaller is better (Best = 0), Range=[0, +inf)

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The Ball-Hall index

Return type:

result (float)

BI(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwarg)

Computes the Beale Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Beale Index

Return type:

result (float)

BRI(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Banfeld-Raftery Index.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Banfeld-Raftery Index

Return type:

result (float)

CDS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Czekanowski-Dice score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Czekanowski-Dice score

Return type:

result (float)

CHI(X=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Compute the Calinski and Harabasz (1974) index. It is also known as the Variance Ratio Criterion. The score is defined as ratio between the within-cluster dispersion and the between-cluster dispersion.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The resulting Calinski-Harabasz index.

Return type:

result (float)

CS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Completeness Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The completeness score.

Return type:

result (float)

DBCVI(X=None, y_pred=None, force_finite=True, finite_value=0.0, return_type='global', **kwarg)

Computes the Density-based Clustering Validation Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

• return_type (str) – The output type. Can be “global”, “per-cluster”, or “both”. Default is “global”.

Returns:

• If “global”: Returns the overall DBCV score (float).

• If “per-cluster”: Returns a dictionary mapping valid cluster labels to their individual validity scores.

• If “both”: Returns a tuple (global_score, per_cluster_dict).

Return type:

float or dict or tuple

DBI(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Davies-Bouldin index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Davies-Bouldin index

Return type:

result (float)

DHI(X=None, y_pred=None, chunk_size=5000, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Duda Index or Duda-Hart index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• chunk_size (int) – Split original data to chunk_size to avoid OOM problem

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Duda-Hart index

Return type:

result (float)

DI(X=None, y_pred=None, use_modified=True, force_finite=True, finite_value=0.0, **kwargs)

Computes the Dunn Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• use_modified (bool) – The modified version we proposed to speed up the computational time for this metric, default=True

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Dunn Index

Return type:

result (float)

DRI(X=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Det-Ratio index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Det-Ratio index

Return type:

result (float)

EnS(y_true=None, y_pred=None, **kwargs)

Computes the Entropy score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Entropy score

Return type:

result (float)

FMS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Fowlkes-Mallows score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Fowlkes-Mallows score

Return type:

result (float)

FS(y_true=None, y_pred=None, beta=1.0, force_finite=True, finite_value=0.0, **kwargs)

Computes the F-Measure score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• beta (float) – The weight parameter, default = 1.0

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The F-Measure score

Return type:

result (float)

GAS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Gamma Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Gamma Score

Return type:

result (float)

GPS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Gplus Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Gplus Score

Return type:

result (float)

HGS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Hubert Gamma score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Hubert Gamma score

Return type:

result (float)

HI(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwarg)

Computes the Hartigan index for a clustering solution.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Hartigan index

Return type:

result (float)

HS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Homogeneity Score

It measures the extent to which each cluster contains only data points that belong to a single class or category. In other words, homogeneity assesses whether all the data points in a cluster are members of the same true class or label. A higher homogeneity score indicates better clustering results, where each cluster corresponds well to a single ground truth class.

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Homogeneity Score

Return type:

result (float)

JS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Jaccard score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Jaccard score

Return type:

result (float)

KDI(X=None, y_pred=None, use_normalized=True, **kwargs)

Computes the Ksq-DetW Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• use_normalized (bool) – We normalize the scatter matrix before calculate the Det to reduce the value, default=True

Returns:

The Ksq-DetW Index

Return type:

result (float)

KS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Kulczynski Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Kulczynski score

Return type:

result (float)

LDRI(X=None, y_pred=None, force_finite=True, finite_value=-10000000000.0, **kwargs)

Computes the Log Det Ratio Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Log Det Ratio Index

Return type:

result (float)

LSRI(X=None, y_pred=None, force_finite=True, finite_value=-10000000000.0, **kwargs)

Computes the Log SS Ratio Index (LSRI).

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Log SS Ratio Index

Return type:

result (float)

MIS(y_true=None, y_pred=None, **kwargs)

Computes the Mutual Information score.

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Mutual Information score

Return type:

result (float)

MNS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Mc Nemar score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Mc Nemar score

Return type:

result (float)

MSEI(X=None, y_pred=None, **kwarg)

Computes the Mean Squared Error Index MSEI measures the mean of squared distances between each data point and its corresponding centroid or cluster center.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The Mean Squared Error Index

Return type:

result (float)

NMIS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the normalized mutual information It is a variation of the mutual information score that normalizes the result to take values between 0 and 1. It is defined as the mutual information divided by the average entropy of the true and predicted clusterings. Bigger is better (Best = 1), Range = [0, 1]

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The normalized mutual information score.

Return type:

result (float)

PhS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Phi score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Phi score

Return type:

result (float)

PrS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Precision Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Precision score

Return type:

result (float)

PuS(y_true=None, y_pred=None, **kwargs)

Computes the Purity score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Purity score

Return type:

result (float)

RRS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Russel-Rao score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Russel-Rao score

Return type:

result (float)

RSI(X=None, y_pred=None, **kwarg)

Computes the R-squared index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The R-squared index

Return type:

result (float)

RTS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Rogers-Tanimoto score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Rogers-Tanimoto score

Return type:

result (float)

RaS(y_true=None, y_pred=None, **kwargs)

Computes the Rand score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The rand score.

Return type:

result (float)

ReS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Recall Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Recall score

Return type:

result (float)

SI(X=None, y_pred=None, multi_output=False, force_finite=True, finite_value=-1.0, chunk_size=5000, **kwargs)

Computes the Silhouette Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• multi_output (bool) – Returned scores for each cluster, default=False

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

• chunk_size (int) – Split original data to chunk_size to avoid OOM problem

Returns:

The Silhouette Index

Return type:

result (float)

SS1S(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Sokal-Sneath 1 score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Sokal-Sneath 1 score

Return type:

result (float)

SS2S(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Sokal-Sneath 2 score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Sokal-Sneath 2 score

Return type:

result (float)

SSEI(X=None, y_pred=None, **kwarg)

Computes the Sum of Squared Error Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The Sum of Squared Error Index

Return type:

result (float)

SUPPORT = {'ARS': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'BHI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'BI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'BRI': {'best': 'unknown', 'range': '(-inf, +inf)', 'type': 'min'}, 'CDS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'CHI': {'best': 'unknown', 'range': '[0, +inf)', 'type': 'max'}, 'CS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'DBCVI': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'DBI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'DHI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'DI': {'best': 'unknown', 'range': '[0, +inf)', 'type': 'max'}, 'DRI': {'best': 'unknown', 'range': '[1, +inf)', 'type': 'max'}, 'EnS': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'FMS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'FS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'GAS': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'GPS': {'best': '0', 'range': '[0, 1]', 'type': 'min'}, 'HGS': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'HI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'HS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'JS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'KDI': {'best': 'unknown', 'range': '(-inf, +inf)', 'type': 'max'}, 'KS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'LDRI': {'best': 'unknown', 'range': '(-inf, +inf)', 'type': 'max'}, 'LSRI': {'best': 'unknown', 'range': '(-inf, +inf)', 'type': 'max'}, 'MIS': {'best': 'unknown', 'range': '[0, +inf)', 'type': 'max'}, 'MNS': {'best': 'unknown', 'range': '(-inf, +inf)', 'type': 'max'}, 'MSEI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'NMIS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'PhS': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'PrS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'PuS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'RRS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'RSI': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'RTS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'RaS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'ReS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'SI': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'SS1S': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'SS2S': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'SSEI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}, 'TauS': {'best': '1', 'range': '[-1, 1]', 'type': 'max'}, 'VMS': {'best': '1', 'range': '[0, 1]', 'type': 'max'}, 'XBI': {'best': '0', 'range': '[0, +inf)', 'type': 'min'}}

TauS(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Tau Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Tau Score

Return type:

result (float)

VMS(y_true=None, y_pred=None, beta=1.0, force_finite=True, finite_value=0.0, **kwargs)

Computes the V Measure Score

It is a combination of two other metrics: homogeneity and completeness. Homogeneity measures whether all the data points in a given cluster belong to the same class. Completeness measures whether all the data points of a certain class are assigned to the same cluster. The V-measure combines these two metrics into a single score.

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• beta (float) – The weight parameter, default = 1.0

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The V measure score

Return type:

result (float)

XBI(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Xie-Beni index.

The Xie-Beni index is an index of fuzzy clustering, but it is also applicable to crisp clustering. The numerator is the mean of the squared distances of all of the points with respect to their barycenter of the cluster they belong to. The denominator is the minimal squared distances between the points in the clusters. The minimum value indicates the best number of clusters.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Xie-Beni index

Return type:

result (float)

adjusted_rand_score(y_true=None, y_pred=None, **kwargs)

Computes the Adjusted rand score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Adjusted rand score

Return type:

result (float)

ball_hall_index(X=None, y_pred=None, **kwargs)

The Ball-Hall Index (1995) is the mean of the mean dispersion across all clusters. The largest difference between successive clustering levels indicates the optimal number of clusters. Smaller is better (Best = 0), Range=[0, +inf)

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The Ball-Hall index

Return type:

result (float)

banfeld_raftery_index(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Banfeld-Raftery Index.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Banfeld-Raftery Index

Return type:

result (float)

beale_index(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwarg)

Computes the Beale Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Beale Index

Return type:

result (float)

calinski_harabasz_index(X=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Compute the Calinski and Harabasz (1974) index. It is also known as the Variance Ratio Criterion. The score is defined as ratio between the within-cluster dispersion and the between-cluster dispersion.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The resulting Calinski-Harabasz index.

Return type:

result (float)

check_X(X)

Validate the structural properties of the feature matrix array X.

Parameters:

X (tuple, list, or np.ndarray, optional) – The input features. If None, uses the instance attribute self.X.

Returns:

The validated 2D NumPy array representation of the dataset.

Return type:

np.ndarray

Raises:

ValueError – If the feature data is missing, not exactly 2-dimensional, or is empty.

completeness_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Completeness Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The completeness score.

Return type:

result (float)

czekanowski_dice_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Czekanowski-Dice score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Czekanowski-Dice score

Return type:

result (float)

davies_bouldin_index(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Davies-Bouldin index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Davies-Bouldin index

Return type:

result (float)

density_based_clustering_validation_index(X=None, y_pred=None, force_finite=True, finite_value=0.0, return_type='global', **kwarg)

Computes the Density-based Clustering Validation Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

• return_type (str) – The output type. Can be “global”, “per-cluster”, or “both”. Default is “global”.

Returns:

• If “global”: Returns the overall DBCV score (float).

• If “per-cluster”: Returns a dictionary mapping valid cluster labels to their individual validity scores.

• If “both”: Returns a tuple (global_score, per_cluster_dict).

Return type:

float or dict or tuple

det_ratio_index(X=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Det-Ratio index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Det-Ratio index

Return type:

result (float)

duda_hart_index(X=None, y_pred=None, chunk_size=5000, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Duda Index or Duda-Hart index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• chunk_size (int) – Split original data to chunk_size to avoid OOM problem

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Duda-Hart index

Return type:

result (float)

dunn_index(X=None, y_pred=None, use_modified=True, force_finite=True, finite_value=0.0, **kwargs)

Computes the Dunn Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• use_modified (bool) – The modified version we proposed to speed up the computational time for this metric, default=True

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Dunn Index

Return type:

result (float)

entropy_score(y_true=None, y_pred=None, **kwargs)

Computes the Entropy score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Entropy score

Return type:

result (float)

f_measure_score(y_true=None, y_pred=None, beta=1.0, force_finite=True, finite_value=0.0, **kwargs)

Computes the F-Measure score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• beta (float) – The weight parameter, default = 1.0

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The F-Measure score

Return type:

result (float)

fowlkes_mallows_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Fowlkes-Mallows score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Fowlkes-Mallows score

Return type:

result (float)

gamma_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Gamma Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Gamma Score

Return type:

result (float)

get_processed_external_data(y_true=None, y_pred=None, force_finite=None, finite_value=None)

Validate, prioritize, and format the ground truth and predicted labels for external metrics.

Parameters:

• y_true (tuple, list, or np.ndarray, optional) – The ground truth class values. If None, uses the instance attribute self.y_true.

• y_pred (tuple, list, or np.ndarray, optional) – The predicted cluster labels. If None, uses the instance attribute self.y_pred.

• force_finite (bool, optional) – Override for the force_finite configuration.

• finite_value (float, optional) – Override for the finite_value fallback configuration.

Returns:

A tuple containing: - y_true_final (np.ndarray): Formatted ground truth labels. - y_pred_final (np.ndarray): Formatted predicted cluster labels. - le (LabelEncoder): The label encoder instance mapping target values. - force_finite (bool): The final finite-forcing flag applied. - finite_value (float or None): The final fallback value applied.

Return type:

tuple

Raises:

ValueError – If either y_true or y_pred is unavailable.

get_processed_internal_data(y_pred=None, force_finite=None, finite_value=None)

Validate, prioritize, and format predicted labels for internal metrics.

Parameters:

• y_pred (tuple, list, or np.ndarray, optional) – The predicted cluster labels. If None, uses the instance attribute self.y_pred.

• force_finite (bool, optional) – Override for the force_finite configuration.

• finite_value (float, optional) – Override for the finite_value fallback configuration.

Returns:

A tuple containing: - y_pred_final (np.ndarray): Formatted predicted cluster labels. - le (LabelEncoder): The label encoder instance. - force_finite (bool): The final finite-forcing flag applied. - finite_value (float or None): The final fallback value applied.

Return type:

tuple

Raises:

ValueError – If y_pred is unavailable.

static get_support(name=None, verbose=True)

Get metadata support information for a specific metric or all metrics.

Parameters:

• name (str, default=None) – The abbreviation of the metric (e.g., ‘DBCVI’, ‘SI’). If ‘all’, returns information for all supported metrics.

• verbose (bool, default=True) – Whether to print the metric details directly to the console.

Returns:

A dictionary containing properties (‘type’, ‘range’, ‘best’) of the requested metric(s).

Return type:

dict

Raises:

ValueError – If the metric name is not supported by the class.

gplus_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Gplus Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Gplus Score

Return type:

result (float)

hartigan_index(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwarg)

Computes the Hartigan index for a clustering solution.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Hartigan index

Return type:

result (float)

homogeneity_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Homogeneity Score

It measures the extent to which each cluster contains only data points that belong to a single class or category. In other words, homogeneity assesses whether all the data points in a cluster are members of the same true class or label. A higher homogeneity score indicates better clustering results, where each cluster corresponds well to a single ground truth class.

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Homogeneity Score

Return type:

result (float)

hubert_gamma_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Hubert Gamma score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Hubert Gamma score

Return type:

result (float)

jaccard_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Jaccard score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Jaccard score

Return type:

result (float)

ksq_detw_index(X=None, y_pred=None, use_normalized=True, **kwargs)

Computes the Ksq-DetW Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• use_normalized (bool) – We normalize the scatter matrix before calculate the Det to reduce the value, default=True

Returns:

The Ksq-DetW Index

Return type:

result (float)

kulczynski_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Kulczynski Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Kulczynski score

Return type:

result (float)

log_det_ratio_index(X=None, y_pred=None, force_finite=True, finite_value=-10000000000.0, **kwargs)

Computes the Log Det Ratio Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Log Det Ratio Index

Return type:

result (float)

log_ss_ratio_index(X=None, y_pred=None, force_finite=True, finite_value=-10000000000.0, **kwargs)

Computes the Log SS Ratio Index (LSRI).

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Log SS Ratio Index

Return type:

result (float)

mc_nemar_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Mc Nemar score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Mc Nemar score

Return type:

result (float)

mean_squared_error_index(X=None, y_pred=None, **kwarg)

Computes the Mean Squared Error Index MSEI measures the mean of squared distances between each data point and its corresponding centroid or cluster center.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The Mean Squared Error Index

Return type:

result (float)

mutual_info_score(y_true=None, y_pred=None, **kwargs)

Computes the Mutual Information score.

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Mutual Information score

Return type:

result (float)

normalized_mutual_info_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the normalized mutual information It is a variation of the mutual information score that normalizes the result to take values between 0 and 1. It is defined as the mutual information divided by the average entropy of the true and predicted clusterings. Bigger is better (Best = 1), Range = [0, 1]

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The normalized mutual information score.

Return type:

result (float)

phi_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Phi score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Phi score

Return type:

result (float)

precision_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Precision Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Precision score

Return type:

result (float)

purity_score(y_true=None, y_pred=None, **kwargs)

Computes the Purity score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The Purity score

Return type:

result (float)

r_squared_index(X=None, y_pred=None, **kwarg)

Computes the R-squared index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The R-squared index

Return type:

result (float)

rand_score(y_true=None, y_pred=None, **kwargs)

Computes the Rand score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

Returns:

The rand score.

Return type:

result (float)

recall_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Recall Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Recall score

Return type:

result (float)

rogers_tanimoto_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Rogers-Tanimoto score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Rogers-Tanimoto score

Return type:

result (float)

russel_rao_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Russel-Rao score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Russel-Rao score

Return type:

result (float)

silhouette_index(X=None, y_pred=None, multi_output=False, force_finite=True, finite_value=-1.0, chunk_size=5000, **kwargs)

Computes the Silhouette Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• multi_output (bool) – Returned scores for each cluster, default=False

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

• chunk_size (int) – Split original data to chunk_size to avoid OOM problem

Returns:

The Silhouette Index

Return type:

result (float)

sokal_sneath1_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Sokal-Sneath 1 score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Sokal-Sneath 1 score

Return type:

result (float)

sokal_sneath2_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Sokal-Sneath 2 score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Sokal-Sneath 2 score

Return type:

result (float)

sum_squared_error_index(X=None, y_pred=None, **kwarg)

Computes the Sum of Squared Error Index

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

Returns:

The Sum of Squared Error Index

Return type:

result (float)

tau_score(y_true=None, y_pred=None, force_finite=True, finite_value=0.0, **kwargs)

Computes the Tau Score

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Tau Score

Return type:

result (float)

v_measure_score(y_true=None, y_pred=None, beta=1.0, force_finite=True, finite_value=0.0, **kwargs)

Computes the V Measure Score

It is a combination of two other metrics: homogeneity and completeness. Homogeneity measures whether all the data points in a given cluster belong to the same class. Completeness measures whether all the data points of a certain class are assigned to the same cluster. The V-measure combines these two metrics into a single score.

Parameters:

• y_true (array-like) – The true labels for each sample.

• y_pred (array-like) – The predicted cluster labels for each sample.

• beta (float) – The weight parameter, default = 1.0

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The V measure score

Return type:

result (float)

xie_beni_index(X=None, y_pred=None, force_finite=True, finite_value=10000000000.0, **kwargs)

Computes the Xie-Beni index.

The Xie-Beni index is an index of fuzzy clustering, but it is also applicable to crisp clustering. The numerator is the mean of the squared distances of all of the points with respect to their barycenter of the cluster they belong to. The denominator is the minimal squared distances between the points in the clusters. The minimum value indicates the best number of clusters.

Parameters:

• X (array-like of shape (n_samples, n_features)) – A list of n_features-dimensional data points. Each row corresponds to a single data point.

• y_pred (array-like of shape (n_samples,)) – Predicted labels for each sample.

• force_finite (bool) – Make result as finite number

• finite_value (float) – The value that used to replace the infinite value or NaN value.

Returns:

The Xie-Beni index

Return type:

result (float)