Feature Robust Optimal Transport for High-dimensional Data
This addresses a bottleneck in applying optimal transport to high-dimensional data, such as in deep learning for semantic correspondence, though it appears incremental as it builds on existing OT methods with feature selection.
The paper tackles the curse of dimensionality in optimal transport for high-dimensional data by proposing feature-robust optimal transport (FROT), which uses feature selection to find discriminative features and a transport plan robust to noise, achieving state-of-the-art performance in real-world semantic correspondence datasets.
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.