Clustering Metrics

• BHI - Ball-Hall Index
• CHI - Calinski-Harabasz Index
• XBI - Xie-Beni Index
• DBI - Davies-Bouldin Index
• BRI - Banfeld-Raftery Index
• DRI - Det-Ratio Index
• KDI - Ksq-DetW Index
• LDRI - Log Det Ratio Index
• DI - Dunn Index
• LSRI - Log SS Ratio Index
• SI - Silhouette Index
• SSEI - Sum of Squared Error Index
• MSEI - Mean Squared Error Index
• DHI - Duda-Hart Index
• BI - Beale Index
• RSI - R-Squared Index
• DBCVI - Density-Based Clustering Validation Index
• HI - Hartigan Index
• MIS - Mutual Information Score
• NMIS - Normalized Mutual Information Score
• RaS - Rand Score
• ARS - Adjusted Rand Score
• FMS - Fowlkes-Mallows Score
• HS - Homogeneity Score
• CS - Completeness Score
• VMS - V-Measure Score
• PrS - Precision Score
• ReS - Recall Score
• FS - F-Measure Score
• CDS - Czekanowski-Dice Score
• HGS - Hubert Gamma Score
• JS - Jaccard Score
• KS - Kulczynski Score
• MNS - McNemar Score
• PhS - Phi Score
• RTS - Rogers-Tanimoto Score
• RRS - Russell-Rao Score
• SS1S & SS2S - Sokal-Sneath Scores
• PuS - Purity Score
• EnS - Entropy Score
• TauS - Tau Score
• GAS - Gamma Score
• GPS - G-Plus Score

All Clustering Metrics

The majority of the clustering metrics in this library are implemented based on the comprehensive study by [33].

There are two primary categories of metrics commonly used to evaluate the quality of clustering results:

• Internal Evaluation Metrics: These metrics evaluate the clustering structure based solely on the intrinsic properties of the data itself, without relying on any external information or ground truth labels. Examples include the Silhouette Coefficient, Calinski-Harabasz Index, and Davies-Bouldin Index.

• External Evaluation Metrics: These metrics assess the clustering results by comparing them to an external reference, such as expert-annotated labels or a gold standard. Examples include the Adjusted Rand Score, Normalized Mutual Information Score, and Fowlkes-Mallows Score.

It is highly recommended to evaluate your models using appropriate metrics tailored to your specific problem domain and data distribution.

Note

Library Naming Convention

To help users easily distinguish between the two evaluation categories, this library strictly enforces the following naming rule:

• Metrics belonging to the internal evaluation category will have the suffix “Index” (e.g., Dunn Index).

• Metrics belonging to the external evaluation category will have the suffix “Score” (e.g., Adjusted Rand Score).

STT	Metric	Metric Fullname	Characteristics
1	BHI	Ball Hall Index	Smaller is better (Best = 0), Range=[0, +inf)
2	XBI	Xie Beni Index	Smaller is better (Best = 0), Range=[0, +inf)
3	DBI	Davies Bouldin Index	Smaller is better (Best = 0), Range=[0, +inf)
4	BRI	Banfeld Raftery Index	Smaller is better (No best value), Range=(-inf, +inf)
5	KDI	Ksq Detw Index	Smaller is better (No best value), Range=(-inf, +inf)
6	DRI	Det Ratio Index	Bigger is better (No best value), Range=[1, +inf)
7	DI	Dunn Index	Bigger is better (No best value), Range=[0, +inf)
8	CHI	Calinski Harabasz Index	Bigger is better (No best value), Range=[0, +inf)
9	LDRI	Log Det Ratio Index	Bigger is better (No best value), Range=(-inf, +inf)
10	LSRI	Log SS Ratio Index	Bigger is better (No best value), Range=(-inf, +inf)
11	SI	Silhouette Index	Bigger is better (Best = 1), Range = [-1, +1]
12	SSEI	Sum of Squared Error Index	Smaller is better (Best = 0), Range = [0, +inf)
13	MSEI	Mean Squared Error Index	Smaller is better (Best = 0), Range = [0, +inf)
14	DHI	Duda-Hart Index	Smaller is better (Best = 0), Range = [0, +inf)
15	BI	Beale Index	Smaller is better (Best = 0), Range = [0, +inf)
16	RSI	R-squared Index	Bigger is better (Best=1), Range = [0, 1]
17	DBCVI	Density-based Clustering Validation Index	Bigger is better (Best=1), Range = [-1, 1]
18	HI	Hartigan Index	Smaller is better (best=0), Range = [0, +inf)
19	MIS	Mutual Info Score	Bigger is better (No best value), Range = [0, +inf)
20	NMIS	Normalized Mutual Info Score	Bigger is better (Best = 1), Range = [0, 1]
21	RaS	Rand Score	Bigger is better (Best = 1), Range = [0, 1]
22	ARS	Adjusted Rand Score	Bigger is better (Best = 1), Range = [-1, 1]
23	FMS	Fowlkes Mallows Score	Bigger is better (Best = 1), Range = [0, 1]
24	HS	Homogeneity Score	Bigger is better (Best = 1), Range = [0, 1]
25	CS	Completeness Score	Bigger is better (Best = 1), Range = [0, 1]
26	VMS	V-Measure Score	Bigger is better (Best = 1), Range = [0, 1]
27	PrS	Precision Score	Bigger is better (Best = 1), Range = [0, 1]
28	ReS	Recall Score	Bigger is better (Best = 1), Range = [0, 1]
29	FS	F-Measure Score	Bigger is better (Best = 1), Range = [0, 1]
30	CDS	Czekanowski Dice Score	Bigger is better (Best = 1), Range = [0, 1]
31	HGS	Hubert Gamma Score	Bigger is better (Best = 1), Range=[-1, 1]
32	JS	Jaccard Score	Bigger is better (Best = 1), Range = [0, 1]
33	KS	Kulczynski Score	Bigger is better (Best = 1), Range = [0, 1]
34	MNS	Mc Nemar Score	Bigger is better (No best value), Range=(-inf, +inf)
35	PhS	Phi Score	Bigger is better (Best = 1), Range = [-1, 1]
36	RTS	Rogers Tanimoto Score	Bigger is better (Best = 1), Range = [0, 1]
37	RRS	Russel Rao Score	Bigger is better (Best = 1), Range = [0, 1]
38	SS1S	Sokal Sneath1 Score	Bigger is better (Best = 1), Range = [0, 1]
39	SS2S	Sokal Sneath2 Score	Bigger is better (Best = 1), Range = [0, 1]
40	PuS	Purity Score	Bigger is better (Best = 1), Range = [0, 1]
41	EnS	Entropy Score	Smaller is better (Best = 0), Range = [0, +inf)
42	TauS	Tau Score	Bigger is better (Best = 1), Range = [-1, 1]
43	GAS	Gamma Score	Bigger is better (Best = 1), Range = [-1, 1]
44	GPS	Gplus Score	Smaller is better (Best = 0), Range = [0, 1]