Low-rank tensor completion: A Riemannian manifold preconditioning approach

Hiroyuki Kasai, Bamdev Mishra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Citations (Scopus)

Abstract

We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry that exists in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian optimization on quotient manifolds to develop preconditioned nonlinear conjugate gradient and stochastic gradient descent algorithms for batch and online setups, respectively. Concrete matrix representations of various optimization-related ingredients are listed. Numerical comparisons suggest that our proposed algorithms robustly outperform state-ofthe-art algorithms across different synthetic and real-world datasets.

Original languageEnglish
Title of host publication33rd International Conference on Machine Learning, ICML 2016
EditorsKilian Q. Weinberger, Maria Florina Balcan
PublisherInternational Machine Learning Society (IMLS)
Pages1576-1606
Number of pages31
ISBN (Electronic)9781510829008
Publication statusPublished - 2016
Externally publishedYes
Event33rd International Conference on Machine Learning, ICML 2016 - New York City, United States
Duration: 2016 Jun 192016 Jun 24

Publication series

Name33rd International Conference on Machine Learning, ICML 2016
Volume3

Conference

Conference33rd International Conference on Machine Learning, ICML 2016
CountryUnited States
CityNew York City
Period16/6/1916/6/24

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Computer Networks and Communications

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  • Cite this

    Kasai, H., & Mishra, B. (2016). Low-rank tensor completion: A Riemannian manifold preconditioning approach. In K. Q. Weinberger, & M. F. Balcan (Eds.), 33rd International Conference on Machine Learning, ICML 2016 (pp. 1576-1606). (33rd International Conference on Machine Learning, ICML 2016; Vol. 3). International Machine Learning Society (IMLS).