Bayesian Robust Tensor Factorization for Incomplete Multiway Data

Qibin Zhao, Guoxu Zhou, Liqing Zhang, Andrzej Cichocki, Shun Ichi Amari

Research output: Contribution to journalArticlepeer-review

128 Citations (Scopus)


We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CANDECOMP/PARAFAC (CP)-rank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The low-CP-rank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior, while the sparse tensor is modeled by a hierarchical view of Student-$t$ distribution that associates an individual hyperparameter with each element independently. For model learning, we develop an efficient variational inference under a fully Bayesian treatment, which can effectively prevent the overfitting problem and scales linearly with data size. In contrast to existing related works, our method can perform model selection automatically and implicitly without the need of tuning parameters. More specifically, it can discover the groundtruth of CP rank and automatically adapt the sparsity inducing priors to various types of outliers. In addition, the tradeoff between the low-rank approximation and the sparse representation can be optimized in the sense of maximum model evidence. The extensive experiments and comparisons with many state-of-the-art algorithms on both synthetic and real-world data sets demonstrate the superiorities of our method from several perspectives.

Original languageEnglish
Article number7120147
Pages (from-to)736-748
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number4
Publication statusPublished - Apr 2016
Externally publishedYes


  • Rank determination
  • robust factorization
  • tensor completion
  • tensor factorization
  • variational Bayesian (VB) inference
  • video background modeling.


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