Exclusive Feature Learning on Arbitrary Structures via $\ell_{1,2}$-norm

Group lasso is widely used to enforce the structural sparsity, which achieves the sparsity at inter-group level. In this paper, we propose a new formulation called ``exclusive group lasso'', which brings out sparsity at intra-group level in the context of feature selection. The proposed exclusive group lasso is applicable on any feature structures, regardless of their overlapping or non-overlapping structures. We give analysis on the properties of exclusive group lasso, and propose an effective iteratively re-weighted algorithm to solve the corresponding optimization problem with rigorous convergence analysis. We show applications of exclusive group lasso for uncorrelated feature selection. Extensive experiments on both synthetic and real-world datasets indicate the good performance of proposed methods.