Structure preservation and distribution alignment in discriminative transfer subspace learning

Abstract

Domain adaptation (DA) is one of the most promising techniques for leveraging existing knowledge from a source domain and applying it to a related target domain. Most DA methods mainly focus on learning a common subspace for the two domains by exploiting either the statistical property or the geometric structure independently to reduce the domain distribution difference. However, these two properties are complementary to each other, and jointly exploring them could yield optimal results. Inspired by the theoretical results of DA, in this paper, we propose structure preservation and distribution alignment (SPDA) in discriminative transfer subspace learning, which embeds the source domain classification error and reduction and domain distribution alignment into a single framework for optimization. SPDA learns an appropriate projection matrix, by which (1) the source domain classification error can be reduced; and (2) the source and target domain data are projected into a common subspace, where the domain distributions are well aligned and each target datum can be linearly reconstructed using the data from the source domain. To reduce the source domain classification error, an ε-dragging technique that relaxes the strict binary label matrix is introduced to enlarge the distance between two data points from different classes. Further, the global subspace structure and the local geometric structure are preserved by imposing a low-rank constraint and a sparse constraint, respectively, on the reconstruction coefficient matrix. Moreover, the space relationship of the samples is preserved using a graph regularization method. In addition, marginal and conditional distributions between the domains are minimized to further reduce the domain shift statistically. We formulate source domain classifier design, geometric structure preservation, and distribution alignment as a rank-minimization problem, and we design an effective optimization algorithm based on the alternating direction method of multipliers (ADMM) to solve this problem. The functions and roles of each term in this framework are analyzed. The results of extensive experiments conducted on five datasets show that SPDA outperforms several state-of-the-art approaches and exhibits classification performance comparable with that of modern deep DA methods.