Homologous Component Analysis for Domain Adaptation

Covariate shift assumption-based domain adaptation approaches usually utilize only one common transformation to align marginal distributions and make conditional distributions preserved. However, one common transformation may cause loss of useful information, such as variances and neighborhood relationship in both source and target domains. To address this problem, we propose a novel method called homologous component analysis (HCA) where we try to find two totally different but homologous transformations to align distributions with side information and make conditional distributions preserved. As it is hard to find a closed-form solution to the corresponding optimization problem, we solve them by means of the alternating direction minimizing method (ADMM) in the context of Stiefel manifolds. We also provide a generalization error bound for domain adaptation in the semi-supervised case, and two transformations can help to decrease this upper bound more than only one common transformation does. Extensive experiments on synthetic and real data show the effectiveness of the proposed method by comparing its classification accuracy with the state-of-the-art methods, and the numerical evidence on chordal distance and Frobenius distance shows that resulting optimal transformations are different.