Sparsity via Sparse Group $k$-max Regularization

• URL: http://arxiv.org/abs/2402.08493v1
• Date: Tue, 13 Feb 2024 14:41:28 GMT
• Title: Sparsity via Sparse Group $k$-max Regularization
• Authors: Qinghua Tao, Xiangming Xi, Jun Xu and Johan A.K. Suykens
• Abstract summary: In this paper, we propose a novel and concise regularization, namely the sparse group $k$-max regularization. We verify the effectiveness and flexibility of the proposed method through numerical experiments on both synthetic and real-world datasets.
• Score: 22.05774771336432
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: For the linear inverse problem with sparsity constraints, the $l_0$ regularized problem is NP-hard, and existing approaches either utilize greedy algorithms to find almost-optimal solutions or to approximate the $l_0$ regularization with its convex counterparts. In this paper, we propose a novel and concise regularization, namely the sparse group $k$-max regularization, which can not only simultaneously enhance the group-wise and in-group sparsity, but also casts no additional restraints on the magnitude of variables in each group, which is especially important for variables at different scales, so that it approximate the $l_0$ norm more closely. We also establish an iterative soft thresholding algorithm with local optimality conditions and complexity analysis provided. Through numerical experiments on both synthetic and real-world datasets, we verify the effectiveness and flexibility of the proposed method.

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