Bayesian Tensor Completion and Decomposition with Automatic CP Rank Determination Using MGP Shrinkage Prior

被引：1
作者：
Takayama H. [1 ]
Zhao Q. [2 ,3 ]
Hontani H. [1 ]
Yokota T. [1 ,2 ]
机构：
[1] Nagoya Institute of Technology, Nagoya
[2] RIKEN Center for Advanced Intelligence Project, Tokyo
[3] Guangdong University of Technology, Guangzhou
来源：
SN Computer Science | 2022年 / 3卷 / 3期
基金：
日本学术振兴会;
关键词：
Bayesian estimation; CP decomposition; MGP shrinkage prior; Tensor completion;
D O I：
10.1007/s42979-022-01119-8
中图分类号：
学科分类号：
摘要：
Tensor completion, which completes high-dimensional data with missing entries, has many applications, such as recommender systems and image inpainting. Low-rank CP decomposition is one of the popular methods in tensor completion and is an extension of matrix decomposition to higher order tensors. However, unlike matrix factorization, it is NP-hard to obtain the rank of CP decomposition directly. In this paper, our objective is simultaneously achieving tensor completion and rank determination in CP decomposition. This can be achieved using Bayesian CP decomposition with Multiplicative Gamma Process (MGP) as the prior distribution. MGP is a distribution that decays the components. Using MGP, the proposed method avoids duplication of components and enables highly accurate rank estimation in Bayesian tensor modeling. In addition, MGP helps to reduce noise sensitivity and estimation time. Numerical experiments using artificial data and image data demonstrate the effectiveness of the proposed method. © 2022, The Author(s).
引用
收藏
相关论文
共 43 条
  • [1] Acar E., Dunlavy D.M., Kolda T.G., Morup M., Scalable tensor factorizations for incomplete data, Chemom Intell Lab Syst, 106, 1, pp. 41-56, (2011)
  • [2] Acar E., Kolda T.G., Dunlavy D.M., . All-at-once optimization for coupled matrix and tensor factorizations, (2011)
  • [3] Bazerque J.A., Mateos G., Giannakis G.B., Rank regularization and Bayesian inference for tensor completion and extrapolation, IEEE Trans Signal Process, 61, 22, pp. 5689-5703, (2013)
  • [4] Bhattacharya A., Dunson D.B., Sparse Bayesian infinite factor models, Biometrika., 98, 2, pp. 291-306, (2011)
  • [5] Bishop C.M., Pattern recognition and machine learning, (2006)
  • [6] Bro R., PARAFAC tutorial and applications, Chemom Intell Lab Syst, 38, 2, pp. 149-172, (1997)
  • [7] Carroll J.D., Chang J.J., Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition, Psychometrika, 35, 3, pp. 283-319, (1970)
  • [8] Chen X., He Z., Sun L., A Bayesian tensor decomposition approach for spatiotemporal traffic data imputation, Transp Res Part C Emerg Technol, 98, pp. 73-84, (2019)
  • [9] Filipovic M., Jukic A., Tucker factorization with missing data with application to low-n-rank tensor completion, Multidimens Syst Signal Process, 26, 3, pp. 677-692, (2015)
  • [10] Gandy S., Recht B., Yamada I., Tensor completion and low-n-rank tensor recovery via convex optimization, Inverse Probl, 27, 2, pp. 025010.1-025010.19, (2011)
12345