## A modified $$k$$-means clustering procedure for obtaining a cardinality-constrained centroid matrix.(English)Zbl 07223613

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.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects)
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