TY - JOUR
T1 - Bayesian Low-Tubal-Rank Robust Tensor Factorization with Multi-Rank Determination
AU - Zhou, Yang
AU - Cheung, Yiu Ming
N1 - Funding Information:
We thank Dr. Jian Lou for helpful discussions. This work was supported by the National Natural Science Foundation of China under Grants: 61672444 and 61272366 and in part by the Faculty Research Grant of Hong Kong Baptist University (HKBU) under Project FRG2/17-18/082, the KTO Grant of HKBU under Project MPCF-004-2017/18, and the SZSTI under Grant JCYJ20160531194006833.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
KW - Bayesian inference
KW - multi-rank determination
KW - Robust PCA
KW - tensor factorization
KW - tubal rank
UR - http://www.scopus.com/inward/record.url?scp=85097571523&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2019.2923240
DO - 10.1109/TPAMI.2019.2923240
M3 - Journal article
C2 - 31226066
AN - SCOPUS:85097571523
SN - 0162-8828
VL - 43
SP - 62
EP - 76
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 1
ER -