  Optimal transport is a machine learning problem with applications including
distribution comparison, feature selection, and generative adversarial
networks. In this paper, we propose feature-robust optimal transport (FROT) for
high-dimensional data, which solves high-dimensional OT problems using feature
selection to avoid the curse of dimensionality. Specifically, we find a
transport plan with discriminative features. To this end, we formulate the FROT
problem as a min--max optimization problem. We then propose a convex
formulation of the FROT problem and solve it using a Frank--Wolfe-based
optimization algorithm, whereby the subproblem can be efficiently solved using
the Sinkhorn algorithm. Since FROT finds the transport plan from selected
features, it is robust to noise features. To show the effectiveness of FROT, we
propose using the FROT algorithm for the layer selection problem in deep neural
networks for semantic correspondence. By conducting synthetic and benchmark
experiments, we demonstrate that the proposed method can find a strong
correspondence by determining important layers. We show that the FROT algorithm
achieves state-of-the-art performance in real-world semantic correspondence
datasets.
