Multi-View Wasserstein Discriminant Analysis with Entropic Regularized Wasserstein Distance

Abstract

Analysis of multi-view data has recently garnered growing attention because multi-view data frequently appear in real-world applications, which are collected or taken from many sources or captured using various sensors. A simple and popular promising approach is to learn a latent subspace shared by multi-view data. Nevertheless, because one sample lies in heterogeneous structure types, many existing multi-view data analyses show that discrepancies in within-class data across multiple views have a larger value than discrepancies within the same view from different views. To evaluate this discrepancy, this paper presents a proposal of a multi-view Wasserstein discriminant analysis, designated as MvWDA, which exploits a recently developed optimal transport theory. Numerical evaluations using three real-world datasets reveal the effectiveness of the proposed MvWDA.