An α -Divergence-Based Approach for Robust Dictionary Learning

In this paper, a robust sequential dictionary learning (DL) algorithm is presented. The proposed algorithm is motivated from the maximum likelihood perspective on dictionary learning and its link to the minimization of the Kullback-Leibler divergence. It is obtained by using a robust loss function in the data fidelity term of the DL objective instead of the usual quadratic loss. The proposed robust loss function is derived from the α -divergence as an alternative to the Kullback-Leibler divergence, which leads to a quadratic loss. Compared to other robust approaches, the proposed loss has the advantage of belonging to class of redescending M-estimators, guaranteeing inference stability from large deviations from the Gaussian nominal noise model. The algorithm is obtained by solving a sequence of penalized rank-1 matrix approximation problems, where the l₁ -norm is introduced as a penalty promoting sparsity and then using a block coordinate descent approach to estimate the unknowns. Performance comparison with similar robust DL algorithms on digit recognition, background removal, and gray-scale image denoising is performed highlighting efficacy of the proposed algorithm.