Robust and high-order correlation alignment for unsupervised domain adaptation

How to measure the domain discrepancy is of significant importance in the field of unsupervised domain adaptation. Among them, Correlation Alignment (CORAL), aligning second-order statistics of source and target domains, has become one of the most widely used discrepancy-based methods. However, the performance of CORAL is limited by: (1) aligning covariance with usual Euclidean metric is suboptimal, and (2) second-order statistics have limited expression for the non-Gaussian distribution. To address these limitations, we propose a Robust Correlation Alignment as well as a High-order Correlation Alignment method. The Robust Correlation Alignment exploits the geometric structure of covariance with matrix square-root normalization. To circumvent unstable and time-consuming properties of the Singular Value Decomposition, we employ the variant of Newton iteration to compute the matrix square-root. Besides, we also propose a High-order Correlation Alignment method, which exploits the third-order statistics for domain alignment. We show that the High-order CORAL can be generalized to Maximum Mean Discrepancy, CORAL and arbitrary-order statistics. Specifically, we propose group matching to reduce space complexity and improve the feasibility in real-world application. Extensive experiments on standard benchmark datasets demonstrate that our proposed methods outperform previous methods by a large margin.