Variational Bayesian Inference for Tensor Robust Principal Component Analysis

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Wang, Chao, Zheng, Huiwen, Chan, Raymond, Wen, Youwei
Format: Preprint
Veröffentlicht: 2024
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866909990035390464
author Wang, Chao
Zheng, Huiwen
Chan, Raymond
Wen, Youwei
author_facet Wang, Chao
Zheng, Huiwen
Chan, Raymond
Wen, Youwei
contents 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 to characterize 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 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_18717
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Variational Bayesian Inference for Tensor Robust Principal Component Analysis
Wang, Chao
Zheng, Huiwen
Chan, Raymond
Wen, Youwei
Numerical Analysis
Machine Learning
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 to characterize 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 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.
title Variational Bayesian Inference for Tensor Robust Principal Component Analysis
topic Numerical Analysis
Machine Learning
url https://arxiv.org/abs/2412.18717