KL property of exponent $1/2$ of $\ell_{2,0}$-norm and DC regularized factorizations for low-rank matrix recovery

Shujun Bi; Ting Tao; Shaohua Pan

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arXiv · 1908.09078

KL property of exponent $1/2$ of $\ell_{2,0}$-norm and DC regularized factorizations for low-rank matrix recovery

Shujun Bi·Ting Tao·Shaohua Pan

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Abstract

This paper is concerned with the factorization form of the rank regularized loss minimization problem. To cater for the scenario in which only a coarse estimation is available for the rank of the true matrix, an $\ell_{2,0}$-norm regularized term is added to the factored loss function to reduce the rank adaptively; and account for the ambiguities in the factorization, a balanced term is then introduced. For the least squares loss, under a restricted condition number assumption on the sampling operator, we establish the KL property of exponent $1/2$ of the nonsmooth factored composite function and its equivalent DC reformulations in the set of their global minimizers. We also confirm the theoretical findings by applying a proximal linearized alternating minimization method to the regularized factorizations.

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Shujun Bi, Ting Tao, Shaohua Pan. 2019-08-24. KL property of exponent $1/2$ of $\ell_{2,0}$-norm and DC regularized factorizations for low-rank matrix recovery. https://arxiv.org/abs/1908.09078

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