Robust Dictionary Learning Using α-Divergence

Abstract

In this paper, a robust sequential dictionary learning (DL) algorithm is presented. 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 for large deviation from the Gaussian nominal noise model. The algorithm is derived via adaptive sequential penalized rank-l matrix approximation using a block coordinate descent approach to obtain the vector pairs of different rank-1 matrices. Performance comparison with similar robust DL algorithms on digit recognition highlights efficacy of the proposed algorithm.