Adaptive sparse and dense hybrid representation with nonconvex optimization

Abstract

Sparse representation has been widely used in signal processing, pattern recognition and computer vision etc. Excellent achievements have been made in both theoretical researches and practical applications. However, there are two limitations on the application of classification. One is that sufficient training samples are required for each class, and the other is that samples should be uncorrupted. In order to alleviate above problems, a sparse and dense hybrid representation (SDR) framework has been proposed, where the training dictionary is decomposed into a class-specific dictionary and a non-class-specific dictionary. SDR puts {\ell }_{\mathrm{1}} constraint on the coefficients of class-specific dictionary. Nevertheless, it over-emphasizes the sparsity and overlooks the correlation information in class-specific dictionary, which may lead to poor classification results. To overcome this disadvantage, an adaptive sparse and dense hybrid representation with nonconvex optimization (ASDR-NO) is proposed in this paper. The trace norm is adopted in class-specific dictionary, which is different from general approaches. By doing so, the dictionary structure becomes adaptive and the representationability of the dictionary will be improved. Meanwhile, a nonconvex surrogate is used to approximate the rank function in dictionary decomposition in order to avoid a suboptimal solution of the original rank minimization, which can be solved by iteratively reweighted nuclear norm (IRNN) algorithm. Extensive experiments conducted on benchmark data sets have verified the effectiveness and advancement of the proposed algorithm compared with the state-of-the-art sparse representation methods.

Keywords

sparse representation / trace norm / nonconvex optimization / low rank matrix recovery / iteratively reweighted nuclear norm

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