Variational Bayesian Inference for Tensor Robust Principal Component Analysis

2024-12-25

AI Summary

Existing tensor robust principal component analysis (TRPCA) methods struggle with inaccurate low-rank structure characterization and poor trade-off control between sparsity and low-rankness under mixed noise. To address these issues, this paper proposes the first variational Bayesian TRPCA framework. Our method introduces a tensor nuclear norm prior and a generalized sparsity-inducing prior, enabling automatic selection of the nuclear norm order and adaptive balancing of low-rank and sparse components; it further incorporates a weighted tensor nuclear norm to enhance structural modeling capability. Extensive experiments on synthetic and real-world datasets demonstrate that our approach significantly outperforms state-of-the-art methods in low-rank recovery accuracy, robustness to mixed noise, and hyperparameter adaptivity. The proposed framework establishes a new paradigm for tensor denoising and decomposition in complex, real-world scenarios.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Intelligent Robots: State Estimation
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Tensor Robust Principal Component Analysis
• Complex Data Handling
• Accuracy Improvement

Innovation

• Variational Bayesian Methods
• Tensor Robust Principal Component Analysis (TRPCA)
• Automatic Tuning