Tensor rank estimation and completion via CP-based nuclear norm

Qiquan Shi, Haiping LU, Yiu Ming CHEUNG*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

17 Citations (Scopus)


Tensor completion (TC) is a challenging problem of recovering missing entries of a tensor from its partial observation. One main TC approach is based on CP/Tucker decomposition. However, this approach often requires the determination of a tensor rank a priori. This rank estimation problem is difficult in practice. Several Bayesian solutions have been proposed but they often under/overestimate the tensor rank while being quite slow. To address this problem of rank estimation with missing entries, we viewthe weight vector of the orthogonal CP decomposition of a tensor to be analogous to the vector of singular values of a matrix. Subsequently, we define a new CP-based tensor nuclear norm as the L1-norm of this weight vector. We then propose Tensor Rank Estimation based on L1-regularized orthogonal CP decomposition (TREL1) for both CP-rank and Tucker-rank. Specifically, we incorporate a regularization with CP-based tensor nuclear norm when minimizing the reconstruction error in TC to automatically determine the rank of an incomplete tensor. Experimental results on both synthetic and real data show that: 1) Given sufficient observed entries, TREL1 can estimate the true rank (both CP-rank and Tucker-rank) of incomplete tensors well; 2) The rank estimated by TREL1 can consistently improve recovery accuracy of decomposition-based TC methods; 3) TREL1 is not sensitive to its parameters in general and more efficient than existing rank estimation methods.

Original languageEnglish
Title of host publicationCIKM 2017 - Proceedings of the 2017 ACM Conference on Information and Knowledge Management
PublisherAssociation for Computing Machinery (ACM)
Number of pages10
ISBN (Electronic)9781450349185
Publication statusPublished - 6 Nov 2017
Event26th ACM International Conference on Information and Knowledge Management, CIKM 2017 - Singapore, Singapore
Duration: 6 Nov 201710 Nov 2017

Publication series

NameInternational Conference on Information and Knowledge Management, Proceedings
VolumePart F131841


Conference26th ACM International Conference on Information and Knowledge Management, CIKM 2017

Scopus Subject Areas

  • Decision Sciences(all)
  • Business, Management and Accounting(all)

User-Defined Keywords

  • CP decomposition
  • CP-based tensor nuclear norm
  • Tensor completion
  • Tensor rank estimation


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