Graph regularized compact self-representative decomposition for image representation

Matrix factorization techniques have been frequently applied in computer vision and pattern recognition. Among them, self-representative matrix decomposition which chooses original data matrix as the dictionary has received considerable attention in dimension reduction and data representation. In this paper, we propose a Graph regularized Compact Self-representative Decomposition (GCSD) method using the linear combination of original data as the dictionary and directly obtaining low dimensional representation of whole data. In GCSD, local geometrical structures are exploited by Laplacian graph, and the global structures are preserved by rank minimization. We develop the iterative updating optimization schemes for GCSD, and provided the convergence proof of our optimization scheme. Experiment results of USPS and COIL20 databases demonstrate the effectiveness of our proposed method.