Low-rank tensor completion: A Riemannian manifold preconditioning approach

Hiroyuki Kasai, Bamdev Mishra

研究成果: Conference contribution

25 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトル33rd International Conference on Machine Learning, ICML 2016
編集者Kilian Q. Weinberger, Maria Florina Balcan
出版社International Machine Learning Society (IMLS)
ページ1576-1606
ページ数31
ISBN(電子版)9781510829008
出版ステータスPublished - 2016
外部発表はい
イベント33rd International Conference on Machine Learning, ICML 2016 - New York City, United States
継続期間: 2016 6 192016 6 24

出版物シリーズ

名前33rd International Conference on Machine Learning, ICML 2016
3

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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