Robust Principal Component Completion

arXiv cs.LG / 3/27/2026

💬 OpinionIdeas & Deep AnalysisModels & Research

共有:

Key Points

The paper introduces robust principal component completion (RPCC), addressing cases where sparse foreground occludes or replaces parts of a low-rank background rather than simply adding sparsely on top.
RPCC identifies the sparse component indirectly by estimating its support, framing the problem using variational Bayesian inference over a fully probabilistic Bayesian sparse tensor factorization.
The method is shown to converge to a hard classifier for the sparse support, avoiding the post-hoc thresholding commonly needed in prior RPCA-based approaches.
Experiments demonstrate near-optimal performance on synthetic data and improved foreground extraction and anomaly detection on real color video and hyperspectral datasets.
The authors provide source code and appendices via the linked GitHub repository, enabling reproduction and further use of the approach.

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.