Classification of histogram-valued data with support histogram machines

Ilsuk Kang, Cheolwoo Park, Young Joo Yoon, Changyi Park, Soon-Sun Kwon and Hosik Choi

Journal of Applied Statistics, 2023, vol. 50, issue 3, 675-690

Abstract: The current large amounts of data and advanced technologies have produced new types of complex data, such as histogram-valued data. The paper focuses on classification problems when predictors are observed as or aggregated into histograms. Because conventional classification methods take vectors as input, a natural approach converts histograms into vector-valued data using summary values, such as the mean or median. However, this approach forgoes the distributional information available in histograms. To address this issue, we propose a margin-based classifier called support histogram machine (SHM) for histogram-valued data. We adopt the support vector machine framework and the Wasserstein-Kantorovich metric to measure distances between histograms. The proposed optimization problem is solved by a dual approach. We then test the proposed SHM via simulated and real examples and demonstrate its superior performance to summary-value-based methods.

Date: 2023
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DOI: 10.1080/02664763.2021.1947996

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