  Traditional dictionary learning methods are based on quadratic convex loss
function and thus are sensitive to outliers. In this paper, we propose a
generic framework for robust dictionary learning based on concave losses. We
provide results on composition of concave functions, notably regarding
super-gradient computations, that are key for developing generic dictionary
learning algorithms applicable to smooth and non-smooth losses. In order to
improve identification of outliers, we introduce an initialization heuristic
based on undercomplete dictionary learning. Experimental results using
synthetic and real data demonstrate that our method is able to better detect
outliers, is capable of generating better dictionaries, outperforming
state-of-the-art methods such as K-SVD and LC-KSVD.
