Classification of Histogram-Valued Data with Support Histogram Machines

• Activity Number: 365 - Contributed Poster Presentations: Korean International Statistical Society
• Type: Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Korean International Statistical Society
• Author(s): Ilsuk Kang* and Cheolwoo Park and Hosik Choi and Young Joo Yoon and Changyi Park
• Companies: University of Georgia and University of Georgia and Kyonggi University and Korea National University of Education and University of Seoul
• Keywords: Histogram-valued data; Support vector machines; Wasserstein-Kantantorvic distance

Abstract

We develop support histogram machines based on the Wasserstein-Kantorovich distance, which can classify histogram-valued data. The main difference of our proposed method from standard SVM is that we use a kernel, designed for histogram-valued data, induced by Wasserstein-Kantorovich distance in the dual form of objective function. Additionally, to mitigate risk of mislabeling due to choice of the ill-suited number of bins, we propose an approach to introduce case-specific parameters into the objective function in order to identify possible mislabels, making our model robust. Simulation results and real data analysis approve adequacy of our method.