Semi-supervised Robust Dictionary Learning via Efficient l-Norms Minimization

Representing the raw input of a data set by a set of relevant codes is crucial to many computer vision applications. Due to the intrinsic sparse property of real-world data, dictionary learning, in which the linear decomposition of a data point uses a set of learned dictionary bases, i.e., codes, has demonstrated state-of-the-art performance. However, traditional dictionary learning methods suffer from three weaknesses: sensitivity to noisy and outlier samples, difficulty to determine the optimal dictionary size, and incapability to incorporate supervision information. In this paper, we address these weaknesses by learning a Semi-Supervised Robust Dictionary (SSR-D). Specifically, we use the l2,0+-norm as the loss function to improve the robustness against outliers, and develop a new structured sparse regularization to incorporate the supervision information in dictionary learning, without incurring additional parameters. Moreover, the optimal dictionary size is automatically learned from the input data. Minimizing the derived objective function is challenging because it involves many non-smooth l2,0+-norm terms. We present an efficient algorithm to solve the problem with a rigorous proof of the convergence of the algorithm. Extensive experiments are presented to show the superior performance of the proposed method.