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Ratio Trace Formulation of Wasserstein Discriminant Analysis
Hexuan Liu · Yunfeng Cai · You-Lin Chen · Ping Li

Mon Dec 07 09:00 PM -- 11:00 PM (PST) @ Poster Session 0 #8

We reformulate the Wasserstein Discriminant Analysis (WDA) as a ratio trace problem and present an eigensolver-based algorithm to compute the discriminative subspace of WDA. This new formulation, along with the proposed algorithm, can be served as an efficient and more stable alternative to the original trace ratio formulation and its gradient-based algorithm. We provide a rigorous convergence analysis for the proposed algorithm under the self-consistent field framework, which is crucial but missing in the literature. As an application, we combine WDA with low-dimensional clustering techniques, such as K-means, to perform subspace clustering. Numerical experiments on real datasets show promising results of the ratio trace formulation of WDA in both classification and clustering tasks.

Author Information

Hexuan Liu (University of Washington)
Yunfeng Cai (Baidu Research)
You-Lin Chen (Department of Statistics, University of Chicago)
Ping Li (Baidu Research USA)

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