Robust Alternating Low-Rank Representation by joint L_p- and L_2,p-norm minimization

We propose a robust Alternating Low-Rank Representation (ALRR) model formed by an alternating forward-backward representation process. For forward representation, ALRR first recovers the low-rank PCs and random corruptions by an adaptive local Robust PCA (RPCA). Then, ALRR performs a joint L_p-norm and L_2,p-norm minimization (0

p-norm on the coefficients can ensure joint sparsity for subspace representation, while the L_2,p-norm on the reconstruction error can handle outlier pursuit. After that, ALRR returns the coefficients as adaptive weights to local RPCA for updating PCs and dictionary in the backward representation process. Thus, ALRR is regarded as an integration of local RPCA with adaptive weights plus sparse LRR with a self-expressive low-rank dictionary. To enable ALRR to handle outside data efficiently, a projective ALRR that can extract features from data directly by embedding is also derived. To solve the L_2,p-norm based minimization problem, a new iterative scheme based on the Iterative Shrinkage/Thresholding (IST) approach is presented. The relationship analysis with other related criteria show that our methods are more general. Visual and numerical results demonstrate the effectiveness of our algorithms for representation.