Transfer subspace learning joint low-rank representation and feature selection

Transfer learning is proposed to solve a general problem in practical applications faced by traditional machine learning methods, that is, the training and test data have different distributions. This paper provides a novel transfer subspace learning method combining low-rank representation (LRR) and feature selection for unsupervised domain adaptation. The core of the proposed method is to map both the source and target data into a latent subspace by a projection such that the discrepancy between domains is reduced. Specifically, by using LRR, a low-rank constraint is imposed on the reconstruction coefficient matrix, and thus the global structure of data can be preserved. Moreover, a structured sparsity-inducing norm based regularization term is introduced into the domain adaptation, which leads to imposing a row-sparsity constraint on the projection matrix. This constraint can enforce rows of the projection matrix corresponding to inessential feature attributes to be all zeros, and thus select relevant features across two domains. As a result, the proposed method has good interpretability and can adaptively perform feature selection. Furthermore, taking into account that the projected samples should be close to each other in the shared subspace if they belong to the same class, regardless of which domain they originally come from, we introduce graph embedding to characterize the local manifold structures of data so as to preserve the relationships between examples in the subspace. Finally, we mathematically formulate the proposed method and derive an iterative algorithm to solve the corresponding problem. The exhaustive experimental evaluations on public datasets confirm the effectiveness of the proposed method in comparison with several state-of-the-art methods.