Unsupervised transfer subspace learning is one of the challenging and important topics in domain adaptation, which aims to classify unlabeled target data by using source domain information. The traditional transfer subspace learning methods often impose low-rank constraints, i.e., trace norm, to preserve data structural information of different domains. However, trace norm is only the convex surrogate to approximate the ideal low-rank constraints and may make their solutions seriously deviate from the original optimums. In addition, the traditional methods directly use the strict labels of source domain, which is difficult to deal with label noise. To solve these problems, we propose a novel nonconvex and discriminative transfer subspace learning method named NDTSL by incorporating Schatten- norm and soft label matrix. Specifically, Schatten- norm can be imposed to approximate the low-rank constraints and obtain a better low-rank representation. Then, we design and adopt soft label matrix in source domain to learn a more flexible classifier and enhance the discriminative ability of target data. Besides, due to the nonconvexity of Schatten- norm, we design an efficient alternative algorithm IALM to solve it. Finally, experimental results on several public transfer tasks demonstrate the effectiveness of NDTSL compared with several state-of-the-art methods.
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