Latent graph-regularized inductive robust principal component analysis

Abstract Recovering low-rank subspaces for data sets becomes an attractive problem in recent years. We proposed a new low-rank subspace learning algorithm, termed latent graph-regularized inductive robust principal component analysis (LGIRPCA), in this paper. Different from the existing low-rank subspace learning methods, LGIRPCA considers the feature manifold structure of a given data set and designs a new Laplacian regularizer to characterize the structure information. We proved that the devised Laplacian regularizer could be transferred to be a weighted sparse constraint for the required low-rank projection matrix. Moreover, the relationships between LGIRPCA and some related algorithms were also discussed. An optimization algorithm based on augmented Lagrange multiplier method was presented to solve LGIRPCA problem. Finally, extensive experiments on several benchmark databases demonstrate the effectiveness of our method for image recover and image classification.