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Error bound of critical points and KL property of exponent $1/2$ for squared F-norm regularized factorization by Tao, Ting; Pan, Shaohua; Bi, Shujun is a scholarly article available to read on EtoBox.

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This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted condition number of the Hessian for the loss function, we derive an error bound to the true matrix for the non-strict critical points with rank not more than that of the true matrix. Then, for the squared F-norm regularized factorized least squares loss function, under the noisy and full sample setting we establish its KL property of exponent $1/2$ on its global minimizer set, and under the noisy and partial sample setting achieve this property for a class of critical points. These theoretical findings are also confirmed by solving the squared F-norm regularized factorization problem with an accelerated alternating minimization method.

Author

Tao, Ting; Pan, Shaohua; Bi, Shujun

Published

2019

Language

EN