A New Representation for Data: Sparse and Low-Rank

Recently, the sparse coding method has been successfully applied in the low-rank subspace clustering algorithm. In these methods, the image is represented as a low-rank linear combination of the atoms of the sparse dictionary, and the coefficient matrix is used to compute the similarity matrix for spectral clustering. However, the low-rank representation obtained by the subspace clustering may not be enough to describe the data structure. In this paper, we propose a new model by combining sparse coding and low-rank subspace clustering in the objective function simultaneously. The new model seeks for solutions which have sparse representation and low-rank representation as close as possible. In this case, the new representation obtained by our method is both sparse and low-rank. An efficient iteratively algorithm is also proposed to solve this model. Extensive experiments on several databases demonstrate that our method performs better than state-of-the-art methods.