Robust Principal Component Completion

TL;DR

The paper introduces a new probabilistic framework called RPCC for robust principal component analysis that improves foreground detection and anomaly detection in videos and hyperspectral data.

Contribution

It proposes a novel Bayesian sparse tensor factorization approach that indirectly identifies the sparse component's support, eliminating the need for post-hoc thresholding.

Findings

Achieves near-optimal estimates on synthetic data.

Provides robust foreground extraction in color videos.

Detects anomalies effectively in hyperspectral datasets.

Abstract

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank background. To address this mismatch, a new framework is proposed in which the sparse component is identified indirectly through determining its support. This approach, called robust principal component completion (RPCC), is solved via variational Bayesian inference applied to a fully probabilistic Bayesian sparse tensor factorization. Convergence to a hard classifier for the support is shown, thereby eliminating the post-hoc thresholding required of most prior RPCA-driven approaches. Experimental results reveal that the proposed approach delivers near-optimal estimates on synthetic data as well as robust foreground-extraction and anomaly-detection performance on real color video and hyperspectral datasets, respectively. Source implementation and Appendices are available at https://github.com/WongYinJ/BCP-RPCC.