393 research outputs found
A Bi-level Nonlinear Eigenvector Algorithm for Wasserstein Discriminant Analysis
Much like the classical Fisher linear discriminant analysis, Wasserstein
discriminant analysis (WDA) is a supervised linear dimensionality reduction
method that seeks a projection matrix to maximize the dispersion of different
data classes and minimize the dispersion of same data classes. However, in
contrast, WDA can account for both global and local inter-connections between
data classes using a regularized Wasserstein distance. WDA is formulated as a
bi-level nonlinear trace ratio optimization. In this paper, we present a
bi-level nonlinear eigenvector (NEPv) algorithm, called WDA-nepv. The inner
kernel of WDA-nepv for computing the optimal transport matrix of the
regularized Wasserstein distance is formulated as an NEPv, and meanwhile the
outer kernel for the trace ratio optimization is also formulated as another
NEPv. Consequently, both kernels can be computed efficiently via
self-consistent-field iterations and modern solvers for linear eigenvalue
problems. Comparing with the existing algorithms for WDA, WDA-nepv is
derivative-free and surrogate-model-free. The computational efficiency and
applications in classification accuracy of WDA-nepv are demonstrated using
synthetic and real-life datasets
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