Deeply Learned Robust Matrix Completion for Large-scale Low-rank Data Recovery

TL;DR

This paper introduces LRMC, a scalable deep learning-based method for robust matrix completion that effectively handles missing data and outliers in large-scale low-rank datasets.

Contribution

It proposes a novel non-convex, learnable approach with deep unfolding and a flexible neural network framework for improved large-scale RMC performance.

Findings

LRMC achieves low computational complexity with linear convergence.

Extensive experiments demonstrate superior performance over state-of-the-art methods.

Effective in applications like video background subtraction and satellite imagery processing.

Abstract

Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable non-convex approach, coined Learned Robust Matrix Completion (LRMC), for large-scale RMC problems. LRMC enjoys low computational complexity with linear convergence. Motivated by the proposed theorem, the free parameters of LRMC can be effectively learned via deep unfolding to achieve optimum performance. Furthermore, this paper proposes a flexible feedforward-recurrent-mixed neural network framework that extends deep unfolding from fix-number iterations to infinite iterations. The superior empirical performance of LRMC is verified with extensive experiments against state-of-the-art on synthetic datasets and real applications, including video background subtraction, ultrasound imaging, face modeling, and cloud removal from satellite imagery.