Ratio Trace Formulation of Wasserstein Discriminant Analysis
Hexuan Liu, Yunfeng Cai, You-Lin Chen, Ping Li
Abstract
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.
BibTeX
@inproceedings{NEURIPS2020_c37f9e12,
author = {Liu, Hexuan and Cai, Yunfeng and Chen, You-Lin and Li, Ping},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
pages = {16821--16832},
publisher = {Curran Associates, Inc.},
title = {Ratio Trace Formulation of Wasserstein Discriminant Analysis},
url = {https://proceedings.neurips.cc/paper_files/paper/2020/file/c37f9e1283cbd4a6edfd778fc8b1c652-Paper.pdf},
volume = {33},
year = {2020}
}