Classification of histogram-valued data with support histogram machines. Issue 3 (17th February 2023)

• Record Type: Journal Article
• Authors: Kang, Ilsuk; Park, Cheolwoo; Yoon, Young Joo; Park, Changyi; Kwon, Soon-Sun; Choi, Hosik
• Is Part Of: Journal of applied statistics. Volume 50:Issue 3(2023)
• Page Start: 675
• Page End: 690
• Publication Date: 2023-02-17
• Subjects: Support vector machines -- symbolic data -- Wasserstein-Kantorovich metric; 62H30; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2021.1947996
• Languages: English
• ISSNs: 0266-4763

Abstract

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.