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Paper Abstract and Keywords
Presentation 2014-07-11 16:40
Derivation of New Update Rules based on KL, Gamma, Renyi Divergences for Nonnegative Matrix Factorization
Masato Seki, Norikazu Takahashi (Okayama Univ) CAS2014-47 VLD2014-56 SIP2014-68 MSS2014-47 SIS2014-47
Abstract (in Japanese) (See Japanese page) 
(in English) Three new update rules based on Kullback-Leibler divergence, gamma-divergence and Renyi divergence for nonnegative matrix factorization are presented in this report. Multiplicative update rules based on these divergences have already been proposed by Yang and Oja. However, their error functions have a common problem that we can increase the values of variables as much as we want while keeping the value of the error function fixed. In addition, the global convergence of their multiplicative update rules is not guaranteed. In order to solve these problems, we add a penalty term to each of the original error functions, and derive three new update rules based on the method of Yang and Oja and the one of Gillis and Glineur. We also prove that the new update rules have the boundedness property which means that any sequence of solutions generated by the new update rules is contained in a bounded region.
Keyword (in Japanese) (See Japanese page) 
(in English) nonnegative matrix factorization / multiplicative update / boundedness / global convergence / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 124, SIP2014-68, pp. 253-258, July 2014.
Paper # SIP2014-68 
Date of Issue 2014-07-02 (CAS, VLD, SIP, MSS, SIS) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
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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 CAS2014-47 VLD2014-56 SIP2014-68 MSS2014-47 SIS2014-47

Conference Information
Committee CAS SIP MSS VLD SIS  
Conference Date 2014-07-09 - 2014-07-11 
Place (in Japanese) (See Japanese page) 
Place (in English) Hokkaido University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) System, signal processing and related topics 
Paper Information
Registration To SIP 
Conference Code 2014-07-CAS-SIP-MSS-VLD-SIS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Derivation of New Update Rules based on KL, Gamma, Renyi Divergences for Nonnegative Matrix Factorization 
Sub Title (in English)  
Keyword(1) nonnegative matrix factorization  
Keyword(2) multiplicative update  
Keyword(3) boundedness  
Keyword(4) global convergence  
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1st Author's Name Masato Seki  
1st Author's Affiliation Okayama University (Okayama Univ)
2nd Author's Name Norikazu Takahashi  
2nd Author's Affiliation Okayama University (Okayama Univ)
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Speaker Author-1 
Date Time 2014-07-11 16:40:00 
Presentation Time 20 minutes 
Registration for SIP 
Paper # CAS2014-47, VLD2014-56, SIP2014-68, MSS2014-47, SIS2014-47 
Volume (vol) vol.114 
Number (no) no.122(CAS), no.123(VLD), no.124(SIP), no.125(MSS), no.126(SIS) 
Page pp.253-258 
#Pages 6 
Date of Issue 2014-07-02 (CAS, VLD, SIP, MSS, SIS) 

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