Error bound of critical points and KL property of exponent 1/2 for squared F-norm regularized factorization

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 restricted condition number of Hessian loss function, we establish an error bound to true non-strict critical points rank not more than that matrix. Then, F-norm factorized least squares its KL property exponent 1/2 global optimal solution set under and full sample setting, achieve this at certain class partial setting. These theoretical findings are also confirmed by solving problem accelerated alternating minimization method.