Feature Robust Optimal Transport for High-dimensional Data

Optimal transport is a machine learning technique 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 aim to select important feature sets and use them to compute the transportation plan. The FROT problem can be formulated as a min--max optimization or a convex minimization problem. Then, we propose a Frank--Wolfe-based optimization algorithm, where the sub-problem can be accurately solved using the Sinkhorn algorithm. An advantage of FROT is that important features can be analytically determined. Furthermore, we propose using the FROT algorithm for feature selection and 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.