Structured Discriminative Dictionary Learning Based on Schatten-p Norm Low-Rank Representation

摘要

Dictionary plays an important role in low-rank representation, which has been widely used to deal with the data contaminated by noise. Traditional low-rank representation relax the non-convex rank minimization problem by the convex nuclear norm minimization, which makes the obtained solution seriously deviate from the practical solution. Meanwhile, the discriminative information between data and dictionary is not effectively exploited. To address these problems, this paper proposed to apply non-convex Schatten-p norm (p = 1/2) to approximate the rank minimization problem. Since Schatten-p norm (p=1/2) is much closer to the rank function than nuclear norm, the proposed strategy can faithfully reflect the essential structure of noisy data. Moreover, a weighted representation regularization term, which encourages to generate a coefficient matrix with class-wise block-diagonal structure, is constructed to enhance the discrimination of dictionary. Experimental results demonstrate advantages of the proposed method over previous dictionary learning methods.