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

arXiv: https://arxiv.org/abs/1911.04293 · HTML: https://mlsanity.com/paper/1911.04293/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2019.

## Built on by (most cited first, 3 of 3)

- [A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization](https://mlsanity.com/paper/2506.20344/) (2025)
- [Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks](https://mlsanity.com/paper/2502.11152/) (2025)
- [Convergence of the majorized PAM method with subspace correction for low-rank composite factorization model](https://mlsanity.com/paper/2406.04588/) (2024)

## Abstract (arXiv)

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.