Group non-convex sparsity regularized partially shared dictionary learning for multi-view learning

Abstract

Multi-view learning aims to obtain more comprehensive understanding than single-view learning by observing objects from different views. However, most existing multi-view learning algorithms are still facing problems in obtaining enough discriminative information from the multi-view data: (1) most models cannot fully exploit consistent and complementary information simultaneously; (2) existing group sparsity based multi-view learning methods cannot extract the most relevant and sparest features. This paper proposes the efficient group non-convex sparsity regularized partially shared dictionary learning for multi-view learning, which employs the partially shared dictionary learning model to excavate both consistency and complementarity simultaneously from the multi-view data, and utilizes the generalized group non-convex sparsity for more discriminative and sparser representations beyond the convex ℓ2,1 norm. To solve the non-convex optimization problem, we derive the generalized optimization framework for different group non-convex sparsity regularizers based on the proximal splitting method. Corresponding proximal operators for structured sparse coding in the framework are derived to form algorithms for different group non-convex sparsity regularizers, i.e., the ℓ2,p (0<p<1) norm and the ℓ2,log regularizer. In experiments, we conduct multi-view clustering in seven real-world multi-view datasets, and performances validate the effectiveness of both group information and non-convexity. Furthermore, results show that appropriate coefficient sharing ratios can help to exploit consistent information while keeping complementary information from multi-view data, thus helping to improve clustering performances. In addition, the convergence performances show that the proposed algorithm can obtain the best clustering performances among compared algorithms and can converge efficiently and stably with reasonable running time costs.