Auto-CVI-Tool , An Automatic Cluster Validity Index Toolbox

Automatic toolbox for Cluster Validity Indexes (CVI) to determine the number of clusters automatically

Auto-CVI-Tool

An Automatic Toolbox for Cluster Validity Indexes (CVI)

A cluster analysis involves identifying the optimal number and natural division of clusters through automatic clustering. A cluster validity index (CVI) is a simple technique for estimating the number of clusters. Several cluster solutions have been proposed in the literature in terms of intra-cluster cohesiveness and inter-cluster separation. In spite of this, it is crucial to identify the situations where these CVIs work well and their limitations. To estimate the number of clusters, this toolbox presents 28 robust CVIs. It is extremely user-friendly and does not require any coding knowledge. Without writing a single line of code, it is possible to compare 28 CVIs and visualize the results in a comparable manner. When the data is loaded, all parameters will be automatically selected by the user, or the default setting will be used, and the CVIs can be compared without any additional programming. It is important to note that one section of this paper was used in the development of this toolbox,I would appreciate a citation to both the reference article and to myself if you use any part of this toolbox.

A cluster validity index (CVI) estimates the quality of a clustering solution by defining a relationship between intracluster cohesiveness (within-group scatter) and intercluster separation (between-group scatter). Table1 summarizes the 22 CVIs examined in this toolbox. Each CVI is identified by an acronym in the table, which is followed by an up arrow ↑ or a down arrow ↓ to indicate whether the index is maximized or minimized, respectively.

Table1

no.	Index	Full Name & Accronym	Min\Max
1	chindex	Calinski-Harabasz index (ch).	↑
2	cindex	C index (cind).	↓
3	copindex	COP index (cop).	↓
4	csindex	CS index (cs).	↓
5	cvddindex	Index based on density-involved distance (cvdd).	↑
6	cvnnindex	Index based on nearest neighbors (cvnn).	↓
7	dbindex	Davies-Bouldin index (db).	↓
8	db2index	Enhanced Davies-Bouldin index (db2).	↓
9	dbcvindex	Density-based index (dbcv).	↑
10	dunnindex	Dunn index (dunn).	↑
11	gd31index	Dunn index variant 3,1 (gd31).	↑
12	gd33index	Dunn index variant 3,3 (gd33).	↑
13	gd41index	Dunn index variant 4,1 (gd41).	↑
14	gd43index	Dunn index variant 4,3 (gd43).	↑
15	gd51index	Dunn index variant 5,1 (gd51).	↑
16	gd53index	Dunn index variant 5,3 (gd53).	↑
17	lccvindex	Index based on local cores (lccv).	↑
18	pbmindex	PBM index (pbm).	↑
19	sdbwindex	S_Dbw validity index (sdbw).	↓
20	sfindex	Score Function index (sf).	↑
21	silindex	Silhouette index (sil).	↑
22	ssddindex	Index based on shapes, sizes, densities, and separation distances (ssdd).	↓
23	svindex	SV index (sv).	↑
24	symindex	Symmetry index (sym).	↑
25	symdbindex	Davies-Bouldin index based on symmetry (sdb).	↓
26	symdunnindex	Dunn index based on symmetry (sdunn).	↑
27	wbindex	WB index (wb).	↓
28	xbindex	Xie-Beni index (xb).	↓

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How to Use?

There are two scripts which are named KMeans_Evaluation.m and Hierarchichal_Evaluation.m; they evalute the clustering based on KMeans and Hierarchichal Clustering resepctively.

• KMeans_Evaluation.m parameter settings
  • data : data
    • load data
  • DistanceKMeans : Distance Type for k-means clustering (Table2)

    • DistanceKMeans = DistKMeans;
      

  • Kmax : Maximum Number of Clusters

    • Kmax = 6; % Maximum Number of Cluster
      clust = zeros(size(data,1),Kmax);
      for k=1:Kmax
         clust(:,k) = kmeans(data,k,'distance',DistanceKMeans);
      end
      

  • CVI : Select form (Table1)

    • %% Select CVI
      CVI = Select_CVI_KMeans;
      % Evaluation of the clustering solutions
      eva = evalcvi(clust,CVI, data);
      

Table2

No.	Distance
2	sqeuclidean
3	cityblock
4	hamming
5	correlation
6	cosine

You may compare multiple CVIs simultaneously by executing the following code:

CVIs = Select_Multiple_CVI_KMeans;
Multiple_Result = Do_Multiple(CVIs,clust,data);

Also it's possible to visualize the reuslt automatically.

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• Hierarchichal_Evaluation.m parameter settings
  • data : data
    • load data
  • HierarchichalMethod : Method for Hierarchical Cluster Tree (Table3)

    •  Z = linkage(data, HierarchichalMethod);
      

  • Kmax : Maximum Number of Clusters

    • Kmax = 6; % Maximum Number of Cluster
      for k=1:Kmax
      clust(:,k) = cluster(Z, 'maxclust', k);
      end
      

  • DistanceType : Type of pairwise distance between two sets of observations (Table4)

    •  DistanceType = Distance_PDIST2;
       DXX = pdist2(data,data,DistanceType);
      

  • CVI : Select form (Table1)

    •  CVI = Select_CVI_Hierarchichal;
       eva = evalcvi(clust,CVI, DXX);
      

If you wish to compare multiple CVIs,run following code

CVIs = Select_Multiple_CVI_Hierarchichal;
Multiple_Result = Do_Multiple(CVIs,clust,DXX);

Table3

No.	Method
2	average
3	centroid
4	complete
5	median
6	single
7	ward

Table4

euclidean	seuclidean
squaredeuclidean	cityblock
minkowski	jaccard
chebychev	mahalanobis
correlation	cosine
spearman	hamming

Visualization

Refrences

(1) A. José-García and W. Gómez-Flores.
    A survey of cluster validity indices for automatic data clustering using differential evolution.
    The Genetic and Evolutionary Computation Conference* (GECCO '21), Lille, France, 2021.
    DOI: 10.1145/3449639.3459341
(2) Farhad Abedinzadeh (2022). Auto-CVI-Tool (https://github.com/farhadabedinzadeh/Auto-CVI-Tool/releases/tag/v1.0.0),
    GitHub. Retrieved October 6, 2022.

Further Question