Structured Sparsity with Group-Graph Regularization

In many learning tasks with structural properties, struc-tural sparsity methods help induce sparse models, usu-ally leading to better interpretability and higher gener-alization performance. One popular approach is to use group sparsity regularization that enforces sparsity on the clustered groups of features, while another popu-lar approach is to adopt graph sparsity regularization that considers sparsity on the link structure of graph embedded features. Both the group and graph struc-tural properties co-exist in many applications. However, group sparsity and graph sparsity have not been consid-ered simultaneously yet. In this paper, we propose a g2-regularization that takes group and graph sparsity into joint consideration, and present an effective approach for its optimization. Experiments on both synthetic and real data show that, enforcing group-graph sparsity lead to better performance than using group sparsity or graph sparsity only