Column $\ell_{2,0}$-norm regularized factorization model of low-rank matrix recovery and its computation

• URL: http://arxiv.org/abs/2008.10466v3
• Date: Sun, 26 Dec 2021 15:07:10 GMT
• Title: Column $\ell_{2,0}$-norm regularized factorization model of low-rank matrix recovery and its computation
• Authors: Ting Tao, Yitian Qian and Shaohua Pan
• Abstract summary: This paper is concerned with the column $ell_2,0$regularized factorization model of low-rank computation problems. Numerical experiments are conducted with synthetic and real data examples.
• Score: 0.9281671380673306
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column sparsity of factors and low-rank solutions. For this nonconvex discontinuous optimization problem, we develop an alternating majorization-minimization (AMM) method with extrapolation, and a hybrid AMM in which a majorized alternating proximal method is proposed to seek an initial factor pair with less nonzero columns and the AMM with extrapolation is then employed to minimize of a smooth nonconvex loss. We provide the global convergence analysis for the proposed AMM methods and apply them to the matrix completion problem with non-uniform sampling schemes. Numerical experiments are conducted with synthetic and real data examples, and comparison results with the nuclear-norm regularized factorization model and the max-norm regularized convex model show that the column $\ell_{2,0}$-regularized factorization model has an advantage in offering solutions of lower error and rank within less time.

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