Classification of histogram-valued data with support histogram machines

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.

Keywords:

• Support vector machines
• symbolic data
• Wasserstein-Kantorovich metric

2010 Mathematics Subject Classification:

• 62H30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Young Joo Yoon was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03028121). The research of Changyi Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2015R1D1A1A01059984). The research of Hosik Choi was supported by the Basic Science Research Program through the NRF funded by the Ministry of Education (2017R1D1A1B05028565).