Feature Selection for Unsupervised Domain Adaptation using Optimal Transport

In this paper, we propose a new feature selection method for unsuper-vised domain adaptation based on the emerging optimal transportation theory. We build upon a recent theoretical analysis of optimal transport in domain adaptation and show that it can directly suggest a feature selection procedure leveraging the shift between the domains. Based on this, we propose a novel algorithm that aims to sort features by their similarity across the source and target domains, where the order is obtained by analyzing the coupling matrix representing the solution of the proposed optimal transportation problem. We evaluate our method on a well-known benchmark data set and illustrate its capability of selecting correlated features leading to better classification performances. Furthermore, we show that the proposed algorithm can be used as a pre-processing step for existing domain adaptation techniques ensuring an important speed-up in terms of the computational time while maintaining comparable results. Finally, we validate our algorithm on clinical imaging databases for computer-aided diagnosis task with promising results.