In recent years, there has been increased interest in symbolic data analysis, including for exploratory analysis, supervised and unsupervised learning, time series analysis, etc. Traditional statistical approaches that are designed to analyze single-valued data are not suitable because they cannot incorporate the additional information on data structure available in symbolic data, and thus new techniques have been proposed for symbolic data to bridge this gap. In this article, we develop a regularized convex clustering approach for grouping histogram-valued data. The convex clustering is a relaxation of hierarchical clustering methods, where prototypes are grouped by having exactly the same value in each group via penalization of parameters. We apply two different distance metrics to measure (dis)similarity between histograms. Various numerical examples confirm that the proposed method shows better performance than other competitors.
Keywords: Wassertein-Kantorovich metric; clustering; histogram-valued data; quantiles; regularization.
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