Classification of histogram-valued data with support histogram machines

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.

Automated summary

This paper focuses on the classification problems when histograms are used as or aggregated into predictors. Conventional classification methods convert histograms into vector-valued data using summary values, which neglect the distributional information in histograms. To address this issue, the authors propose a margin-based classifier named support histogram machine (SHM) utilizing the support vector machine framework and the Wasserstein-Kantorovich metric. The experimental results demonstrate the superior performance of SHM compared to summary-value-based methods.