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Classification of histogram-valued data with support histogram machines

Author

Listed:
  • Ilsuk Kang
  • Cheolwoo Park
  • Young Joo Yoon
  • Changyi Park
  • Soon-Sun Kwon
  • Hosik Choi

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.

Suggested Citation

  • Ilsuk Kang & Cheolwoo Park & Young Joo Yoon & Changyi Park & Soon-Sun Kwon & Hosik Choi, 2023. "Classification of histogram-valued data with support histogram machines," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(3), pages 675-690, February.
    • Handle: RePEc:taf:japsta:v:50:y:2023:i:3:p:675-690
    DOI: 10.1080/02664763.2021.1947996
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