Welcome to Permetrics’s documentation!

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PerMetrics is a python library for performance metrics of machine learning models. We aim to implement all performance metrics for problems such as regression, classification, clustering, … problems. Helping users in all field access metrics as fast as possible

  • Free software: GNU General Public License (GPL) V3 license

  • Total metrics: 112 (48 regression metrics, 20 classification metrics, 44 clustering metrics)

  • Documentation: https://permetrics.readthedocs.io/en/latest/

  • Python versions: >= 3.11

  • Dependencies: numpy, scipy

Models Document

[1]

Thieu Nguyen, Giang Nguyen, and Binh Minh Nguyen. Eo-cnn: an enhanced cnn model trained by equilibrium optimization for traffic transportation prediction. Procedia Computer Science, 176:800–809, 2020.

[2]

Thieu Nguyen, Nhuan Tran, Binh Minh Nguyen, and Giang Nguyen. A resource usage prediction system using functional-link and genetic algorithm neural network for multivariate cloud metrics. In 2018 IEEE 11th conference on service-oriented computing and applications (SOCA), 49–56. IEEE, 2018.

[3]

Takeyoshi Kato. Prediction of photovoltaic power generation output and network operation. In Integration of Distributed Energy Resources in Power Systems, pages 77–108. Elsevier, 2016.

[4]

Thieu Nguyen, Binh Minh Nguyen, and Giang Nguyen. Building resource auto-scaler with functional-link neural network and adaptive bacterial foraging optimization. In International Conference on Theory and Applications of Models of Computation, 501–517. Springer, 2019.

[5]

Timothy O Hodson, Thomas M Over, and Sydney S Foks. Mean squared error, deconstructed. Journal of Advances in Modeling Earth Systems, 13(12):e2021MS002681, 2021.

[6]

Binh Minh Nguyen, Trung Tran, Thieu Nguyen, and Giang Nguyen. An improved sea lion optimization for workload elasticity prediction with neural networks. International Journal of Computational Intelligence Systems, 15(1):90, 2022.

[7]

Thieu Nguyen, Bao Hoang, Giang Nguyen, and Binh Minh Nguyen. A new workload prediction model using extreme learning machine and enhanced tug of war optimization. Procedia Computer Science, 170:362–369, 2020.

[8]

Long-Range Forecasting. From crystal ball to computer. Scott Armstrong Robert J. Genetski, 1978.

[9]

Spyros Makridakis. Accuracy measures: theoretical and practical concerns. International journal of forecasting, 9(4):527–529, 1993.

[10]

Sungil Kim and Heeyoung Kim. A new metric of absolute percentage error for intermittent demand forecasts. International journal of forecasting, 32(3):669–679, 2016.

[11]

Rob J Hyndman and Anne B Koehler. Another look at measures of forecast accuracy. International journal of forecasting, 22(4):679–688, 2006.

[12]

Chengyu Xie, Hoang Nguyen, Xuan-Nam Bui, Van-Thieu Nguyen, and Jian Zhou. Predicting roof displacement of roadways in underground coal mines using adaptive neuro-fuzzy inference system optimized by various physics-based optimization algorithms. Journal of Rock Mechanics and Geotechnical Engineering, 13(6):1452–1465, 2021.

[13]

Ali Najah Ahmed, To Van Lam, Nguyen Duy Hung, Nguyen Van Thieu, Ozgur Kisi, and Ahmed El-Shafie. A comprehensive comparison of recent developed meta-heuristic algorithms for streamflow time series forecasting problem. Applied Soft Computing, 105:107282, 2021.

[14]

Rodrigo Dlugosz da Silva, Marcelo Augusto de Aguiar, Marcelo Giovanetti Canteri, Juliandra Rodrigues Rosisca, Nilson Aparecido Vieira Junio, and others. Reference evapotranspiration for londrina, paraná, brazil: performance of different estimation methods. Semina: Ciências Agrárias, 38(4):2363–2374, 2017.

[15]

Nguyen Van Thieu, Surajit Deb Barma, To Van Lam, Ozgur Kisi, and Amai Mahesha. Groundwater level modeling using augmented artificial ecosystem optimization. Journal of Hydrology, 617:129034, 2023.

[16]

Binh Minh Nguyen, Bao Hoang, Thieu Nguyen, and Giang Nguyen. Nqsv-net: a novel queuing search variant for global space search and workload modeling. Journal of Ambient Intelligence and Humanized Computing, 12:27–46, 2021.

[17]

Edward W Frees, Glenn Meyers, and A David Cummings. Summarizing insurance scores using a gini index. Journal of the American Statistical Association, 106(495):1085–1098, 2011.

[18]

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

[19]

John R Hershey and Peder A Olsen. Approximating the kullback leibler divergence between gaussian mixture models. In 2007 IEEE International Conference on Acoustics, Speech and Signal Processing-ICASSP'07, volume 4, IV–317. IEEE, 2007.

[20]

Bent Fuglede and Flemming Topsoe. Jensen-shannon divergence and hilbert space embedding. In International symposium onInformation theory, 2004. ISIT 2004. Proceedings., 31. IEEE, 2004.

[21]

J Scott Armstrong and Fred Collopy. Error measures for generalizing about forecasting methods: empirical comparisons. International journal of forecasting, 8(1):69–80, 1992.

[22]

Karl G Jöreskog. Structural analysis of covariance and correlation matrices. Psychometrika, 43(4):443–477, 1978.

[23]

Rolla Almodfer, Mohamed E Zayed, Mohamed Abd Elaziz, Moustafa M Aboelmaaref, Mohammed Mudhsh, and Ammar H Elsheikh. Modeling of a solar-powered thermoelectric air-conditioning system using a random vector functional link network integrated with jellyfish search algorithm. Case Studies in Thermal Engineering, 31:101797, 2022.

[24]

Jacob Cohen. A coefficient of agreement for nominal scales. Educational and psychological measurement, 20(1):37–46, 1960.

[25]

Haibo He and Edwardo A Garcia. Learning from imbalanced data. IEEE Transactions on knowledge and data engineering, 21(9):1263–1284, 2009.

[26]

Miroslav Kubat. Addressing the curse of imbalanced training sets: one-sided selection. In Proceedings of the 14th international conference on machine learning, 179–186. Morgan Kaufmann, 1997.

[27]

Davide Chicco and Giuseppe Jurman. The advantages of the matthews correlation coefficient (mcc) over f1 score and accuracy in binary classification evaluation. BMC genomics, 21(1):6, 2020.

[28]

Tom Fawcett. An introduction to roc analysis. Pattern recognition letters, 27(8):861–874, 2006.

[29]

Koby Crammer and Yoram Singer. On the algorithmic implementation of multiclass kernel-based vector machines. Journal of machine learning research, 2(Dec):265–292, 2001.

[30]

Solomon Kullback and Richard A Leibler. On information and sufficiency. The annals of mathematical statistics, 22(1):79–86, 1951.

[31]

W Brier Glenn and others. Verification of forecasts expressed in terms of probability. Monthly weather review, 78(1):1–3, 1950.

[32]

Anqi Mao, Mehryar Mohri, and Yutao Zhong. Cross-entropy loss functions: theoretical analysis and applications. In International conference on Machine learning, 23803–23828. pmlr, 2023.

[33]

Bernard Desgraupes. Clustering indices. University of Paris Ouest-Lab Modal’X, 1(1):34, 2013.

[34]

Tadeusz Caliński and Jerzy Harabasz. A dendrite method for cluster analysis. Communications in Statistics-theory and Methods, 3(1):1–27, 1974.

[35]

Xuanli Lisa Xie and Gerardo Beni. A validity measure for fuzzy clustering. IEEE Transactions on pattern analysis and machine intelligence, 13(8):841–847, 1991.

[36]

David L Davies and Donald W Bouldin. A cluster separation measure. IEEE transactions on pattern analysis and machine intelligence, pages 224–227, 1979.

[37]

Jeffrey D Banfield and Adrian E Raftery. Model-based gaussian and non-gaussian clustering. Biometrics, pages 803–821, 1993.

[38]

Herman P Friedman and Jerrold Rubin. On some invariant criteria for grouping data. Journal of the American Statistical Association, 62(320):1159–1178, 1967.

[39]

Allen J Scott and Michael J Symons. Clustering methods based on likelihood ratio criteria. Biometrics, pages 387–397, 1971.

[40]

Joseph C Dunn. Well-separated clusters and optimal fuzzy partitions. Journal of cybernetics, 4(1):95–104, 1974.

[41]

Peter J Rousseeuw. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of computational and applied mathematics, 20:53–65, 1987.

[42]

Anthony WF Edwards and Luigi Luca Cavalli-Sforza. A method for cluster analysis. Biometrics, pages 362–375, 1965.

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D. N. Sparks. Euclidean cluster analysis. Journal of the Royal Statistical Society Series C: Applied Statistics, 22(1):126–130, 03 1973. URL: https://doi.org/10.2307/2346321, doi:10.2307/2346321.

[44]

Thomas M Cover and Joy A Thomas. Elements of information theory (wiley series in telecommunications and signal processing). Wiley-interscience, 2006.