期刊
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
卷 43, 期 1, 页码 62-76出版社
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2019.2923240
关键词
Robust PCA; tensor factorization; tubal rank; multi-rank determination; Bayesian inference
资金
- National Natural Science Foundation of China [61672444, 61272366]
- Faculty Research Grant of Hong Kong Baptist University (HKBU) [FRG2/17-18/082]
- KTO Grant of HKBU [MPCF-004-2017/18]
- SZSTI [JCYJ20160531194006833]
A new robust tensor factorization method is proposed, which can automatically determine the tensor rank and infer the trade-off between low-rank and sparse components. By Bayesian treatment and a generalized sparsity-inducing prior, the method excels in preserving low-rank structures and image processing.
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.
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