Sparse Group Feature Selection by Weighted Thresholding Homotopy Method

In this paper, we investigate the sparse group feature selection problem, in which covariates posses a grouping structure sparsity at the level of both features and groups simultaneously. We reformulate the feature sparsity constraint as an equivalent weighted l1-norm constraint in the sparse group optimization problem. To solve the reformulated problem, we first propose a weighted thresholding method based on a dynamic programming algorithm. Then we improve the method to a weighted thresholding homotopy algorithm using homotopy technique. We prove that the algorithm converges to an L-stationary point of the original problem. Computational experiments on synthetic data show that the proposed algorithm is competitive with some state-of-the-art algorithms.