Variational Bayesian Inference for Tensor Robust Principal Component Analysis

• URL: http://arxiv.org/abs/2412.18717v1
• Date: Wed, 25 Dec 2024 00:29:09 GMT
• Title: Variational Bayesian Inference for Tensor Robust Principal Component Analysis
• Authors: Chao Wang, Huiwen Zheng, Raymond Chan, Youwen Wen,
• Abstract summary: Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors. We introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. Our method can be efficiently extended to the weighted tensor nuclear norm model.
• Score: 2.6623354466198412
• License:
• Abstract: Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and characterizing the sparse structures of noise. Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors and balancing the trade-off between low-rank and sparse components, especially in a mixed-noise scenario. To address these challenges, we introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. By embedding the proposed priors within the Bayesian framework, our method can automatically determine the optimal tensor nuclear norm and achieve a balance between the nuclear norm and sparse components. Furthermore, our method can be efficiently extended to the weighted tensor nuclear norm model. Experiments conducted on synthetic and real-world datasets demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches.

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