Journal
BIOMETRICS
Volume 75, Issue 2, Pages 603-612Publisher
WILEY
DOI: 10.1111/biom.13004
Keywords
clustering; histogram-valued data; quantiles; regularization; Wassertein-Kantorovich metric
Funding
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Education [2017R1D1A1B05028565, 2017R1D1A1B03028121]
- Bureau of Justice Assistance [2016-PM-BX-K005]
- National Research Foundation of Korea [2017R1D1A1B03028121, 2017R1D1A1B05028565] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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.
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