Bayesian Low-Tubal-Rank Robust Tensor Factorization with Multi-Rank Determination

Yang Zhou, Yiu Ming CHEUNG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Robust tensor factorization is a fundamental problem in machine learning and computer vision, which aims at decomposing tensors into low-rank and sparse components. However, existing methods either suffer from limited modeling power in preserving low-rank structures, or have difficulties in determining the target tensor rank and the trade-off between the low-rank and sparse components. To address these problems, we propose a fully Bayesian treatment of robust tensor factorization along with a generalized sparsity-inducing prior. By adapting the recently proposed low-tubal-rank model in a generative manner, our method is effective in preserving low-rank structures. Moreover, benefiting from the proposed prior and the Bayesian framework, the proposed method can automatically determine the tensor rank while inferring the trade-off between the low-rank and sparse components. For model estimation, we develop a variational inference algorithm, and further improve its efficiency by reformulating the variational updates in the frequency domain. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of the proposed method in multi-rank determination as well as its superiority in image denoising and background modeling over state-of-the-art approaches.

Original languageEnglish
Article number8740980
Pages (from-to)62-76
Number of pages15
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume43
Issue number1
DOIs
Publication statusPublished - 1 Jan 2021

Scopus Subject Areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

User-Defined Keywords

  • Bayesian inference
  • multi-rank determination
  • Robust PCA
  • tensor factorization
  • tubal rank

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