A Modified k-Means Clustering Procedure for Obtaining a Cardinality-Constrained Centroid Matrix

k -means clustering is a well-known procedure for classifying multivariate observations. The resulting centroid matrix of clusters by variables is noted for interpreting which variables characterize clusters. However, between-clusters differences are not always clearly captured in the centroid matri...

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Bibliographic Details
Published in:Journal of classification 2020-07, Vol.37 (2), p.509-525
Main Authors: Yamashita, Naoto, Adachi, Kohei
Format: Article
Language:English
Subjects:
Bioinformatics
Centroids
Cluster analysis
Clustering
Computer simulation
Iterative algorithms
Marketing
Mathematics and Statistics
Optimization
Pattern Recognition
Psychometrics
Signal,Image and Speech Processing
Statistical Theory and Methods
Statistics
Vector quantization
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Summary:k -means clustering is a well-known procedure for classifying multivariate observations. The resulting centroid matrix of clusters by variables is noted for interpreting which variables characterize clusters. However, between-clusters differences are not always clearly captured in the centroid matrix. We address this problem by proposing a new procedure for obtaining a centroid matrix, so that it has a number of exactly zero elements. This allows easy interpretation of the matrix, as we may focus on only the nonzero centroids. The development of an iterative algorithm for the constrained minimization is described. A cardinality selection procedure for identifying the optimal cardinality is presented, as well as a modified version of the proposed procedure, in which some restrictions are imposed on the positions of nonzero elements. The behaviors of our proposed procedure were evaluated in simulation studies and are illustrated with three real data examples, which demonstrate that the performances of the procedure is promising.
ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-019-09324-6