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Paper Abstract and Keywords
Presentation 2016-01-29 15:45
Riemannian preconditioning for tensor completion
Hiroyuki Kasai (UEC), Bamdev Mishra (Uni. of Cambridge, Uni. of Li`ege, Amazon Dev. Cent. India) MoNA2015-50
Abstract (in Japanese) (See Japanese page) 
(in English) We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint. A Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian optimization on quotient manifolds to develop a preconditioned nonlinear conjugate gradient algorithm for the problem. To this end, concrete matrix representations of various optimization-related ingredients are listed. Numerical comparisons suggest that our proposed algorithm robustly outperforms state-of-the-art algorithms across different problem instances encompassing various synthetic and real-world datasets.
Keyword (in Japanese) (See Japanese page) 
(in English) Riemannian optimization / Structured symmetry / Least-squares / Tailored Riemannian metric / Quotient Manifold / Tucker decomposition / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 436, MoNA2015-50, pp. 55-60, Jan. 2016.
Paper # MoNA2015-50 
Date of Issue 2016-01-21 (MoNA) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF MoNA2015-50

Conference Information
Committee MICT ASN MoNA  
Conference Date 2016-01-28 - 2016-01-29 
Place (in Japanese) (See Japanese page) 
Place (in English) Hotel Okada 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Ambient intelligence, ICT for Medical, Healthcare and Sports, etc 
Paper Information
Registration To MoNA 
Conference Code 2016-01-MICT-ASN-MoNA 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Riemannian preconditioning for tensor completion 
Sub Title (in English)  
Keyword(1) Riemannian optimization  
Keyword(2) Structured symmetry  
Keyword(3) Least-squares  
Keyword(4) Tailored Riemannian metric  
Keyword(5) Quotient Manifold  
Keyword(6) Tucker decomposition  
Keyword(7)  
Keyword(8)  
1st Author's Name Hiroyuki Kasai  
1st Author's Affiliation The University of Electro-Communications (UEC)
2nd Author's Name Bamdev Mishra  
2nd Author's Affiliation University of Cambridge, University of Li`ege, Amazon Development Centre India (Uni. of Cambridge, Uni. of Li`ege, Amazon Dev. Cent. India)
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Speaker Author-1 
Date Time 2016-01-29 15:45:00 
Presentation Time 25 minutes 
Registration for MoNA 
Paper # MoNA2015-50 
Volume (vol) vol.115 
Number (no) no.436 
Page pp.55-60 
#Pages 6 
Date of Issue 2016-01-21 (MoNA) 

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