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.

Furthermore, LDStack is amenable to linear systems theory.

Flatness of the loss curve is conjectured to be connected to the generalization ability of machine learning models, in particular neural networks.

Flatness of the loss curve is conjectured to be connected to the generalization ability of machine learning models, in particular neural networks.

Learning has become a core component of the modern information systems we increasingly rely upon to select job candidates, analyze medical data, and control "smart" applications (home, grid, city).

Learning has become a core component of the modern information systems we increasingly rely upon to select job candidates, analyze medical data, and control "smart" applications (home, grid, city).