# Robust Matrix Completion via Maximum Correntropy Criterion and Half Quadratic Optimization

## TL;DR

This paper introduces a robust matrix completion method using maximum correntropy criterion and half-quadratic optimization, which enhances noise robustness and computational efficiency over traditional $l_2$-norm based approaches.

## Contribution

It proposes a novel MCC-based robust matrix completion framework with efficient algorithms that avoid SVD computations and include an adaptive kernel strategy for faster convergence.

## Key findings

- Outperforms existing robust matrix completion algorithms in simulations.
- Avoids SVD at each iteration, reducing computational cost.
- Achieves better noise robustness and convergence speed.

## Abstract

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In this paper, we propose a novel and fast robust matrix completion method based on maximum correntropy criterion (MCC). The correntropy based error measure is utilized instead of using $l_2$-based error norm to improve the robustness to noises. Using the half-quadratic optimization technique, the correntropy based optimization can be transformed to a weighted matrix factorization problem. Then, two efficient algorithms are derived, including alternating minimization based algorithm and alternating gradient descend based algorithm. The proposed algorithms do not need to calculate singular value decomposition (SVD) at each iteration. Further, the adaptive kernel selection strategy is proposed to accelerate the convergence speed as well as improve the performance. Comparison with existing robust matrix completion algorithms is provided by simulations, showing that the new methods can achieve better performance than existing state-of-the-art algorithms.