Convex Clustering Analysis for Histogram-Valued Data

• Activity Number: 175 - Clustering and Changepoint Analysis
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Korean International Statistical Society
• Author(s): Cheolwoo Park* and Hosik Choi and Chris Delcher and Yanning Wang and Youngjoo Yoon
• Companies: University of Georgia and Kyonggi University and University of Florida and University of Florida and Korea National University of Education
• Keywords: Clustering; Histogram-valued data; Quantiles; Regularization; Wassertein-Kantorovich metric

Abstract

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 work, 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.