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.

翻译：本文涉及对噪音低级矩阵回收问题的正方F(robenius)-规范规范化的正常化系数化系数化表。根据对赫西安人损失函数限制条件数的适当假设,我们得出一个与非限制临界点的真正矩阵挂钩的错误,其排名不超过真实矩阵的等级。然后,对于正方F(robenius)-规范化最低系数损失函数,在吵闹和完整的抽样设置下,我们在其全球最小化器集中确定了其KL(Expentent $1/2美元)的财产,在吵闹和部分抽样设置下,为一组临界点实现了这一属性。这些理论结论也通过以加速交替最小化方法解决方F-规范化的正常化系数化问题而得到证实。