Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection

TL;DR

This paper introduces Learned Robust PCA (LRPCA), a scalable deep unfolding method for high-dimensional outlier detection that outperforms existing algorithms and includes a novel infinite-iteration neural network extension.

Contribution

The paper presents a novel deep unfolding-based approach for robust PCA that is scalable, learnable, and extends to infinite iterations with a new neural network model.

Findings

LRPCA outperforms state-of-the-art RPCA algorithms on synthetic and real data.

The method provides recovery guarantees under mild assumptions.

LRPCA is highly efficient and effectively learns parameters through deep unfolding.

Abstract

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for high-dimensional RPCA problems, which we call Learned Robust PCA (LRPCA). LRPCA is highly efficient, and its free parameters can be effectively learned to optimize via deep unfolding. Moreover, we extend deep unfolding from finite iterations to infinite iterations via a novel feedforward-recurrent-mixed neural network model. We establish the recovery guarantee of LRPCA under mild assumptions for RPCA. Numerical experiments show that LRPCA outperforms the state-of-the-art RPCA algorithms, such as ScaledGD and AltProj, on both synthetic datasets and real-world applications.