Feature Robust Optimal Transport for High-dimensional Data

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 jointly solves feature selection and OT problems. Specifically, we formulate the FROT problem as a min--max optimization problem. Then, we propose a convex formulation of FROT and solve it with the Frank--Wolfe-based optimization algorithm, where the sub-problem can be efficiently solved using the Sinkhorn algorithm. A key advantage of FROT is that important features can be analytically determined by simply solving the convex optimization problem. Furthermore, 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 determine important features. Additionally, we show that the FROT algorithm achieves a state-of-the-art performance in real-world semantic correspondence datasets.