SPARK: A New Clustering Algorithm for Obtaining Sparse and Interpretable Centroids

Abstract

k-means clustering is one of the popular procedures for multivariate analysis in which observations are classified into a reduced number of clusters. The resulting centroid matrix is refereed to capture variables which characterize clusters, but between-clusters contrasts in the centroid matrix are not always clear and thus difficult to interpret. In this research, we address the problem in interpretation and propose a new procedure of k-means clustering which produces a sparse and thus interpretable centroid matrix. The proposed procedure is called SPARK. In SPARK, the sparseness of the centroid matrix is constrained and therefore it contains a number of exact zero elements. Because of this, the contrasts between-clusters are highlighted and it allows us to interpret clusters easier in comparison with the standard k-means clustering. A sparsity selection procedure for determining the optimal sparsity of the centroid with reduced computational load is also proposed. Behaviors of the proposed procedure are evaluated by two real data examples, and the results indicate that SPARK performs well for dealing with real world problems.