Sparse representation based on matrix rank minimization and k-means clustering for recognition

In this paper, we propose a sparse coding algorithm based on matrix rank minimization and k-means clustering and for recognition. We consider the problem of removing the noise in the training samples and generating more samples at the same time. To accomplish this, we extended the matrix rank minimization problem to cope with complex data. Samples from the same class are segmented into several groups by k-means clustering algorithm, and matrix rank minimization is applied on the clustered data to separate the noises and recover the low-rank structures in the grouped data. An over-complete dictionary is constructed by connecting the low-rank structures and the training samples together to keep the samples diversity. Sparse representation is operated based on this over-complete dictionary for recognition. Furthermore, a parameter is introduced to adjust the weighting of the coefficients that code the noises. We apply the proposed algorithm for character and face recognition. Experiments with improved performances validate the effectiveness of the proposed algorithm.