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Paper Abstract and Keywords
Presentation 2015-10-05 11:35
Derivation of Multiplicative Update for Constrained Optimization Problems Related to NMF and Its Global Convergence Analysis
Masato Seki, Norikazu Takahashi (Okayama Univ.) CAS2015-24 NLP2015-85
Abstract (in Japanese) (See Japanese page) 
(in English) Nonnegative matrix factorization (NMF) is an operation that decomposes a given nonnegative matrix into two nonnegative factor matrices. It has been successfully applied to speech signal processing, clustering, data mining, and so on. NMF is formulated as an optimization problem to minimize an error function under the nonnegativity constraints on all variables. Among several methods for solving this optimization problem, the multiplicative updates are the most well known and widely used. In this report, we consider a class of constrained optimization problems closely related to NMF. We first derive a multiplicative update rule for these problems by using the unified method developed by Yang and Oja. We next prove that a slightly modified version of the update rule has the global convergence property under certain conditions. This result can be applied not only to representative error functions for NMF but also to a wide class of error functions.
Keyword (in Japanese) (See Japanese page) 
(in English) nonnegative matrix factorization / multiplicative update / global convergence / generalized polynomial / / / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 240, NLP2015-85, pp. 21-26, Oct. 2015.
Paper # NLP2015-85 
Date of Issue 2015-09-28 (CAS, NLP) 
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)
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Conference Information
Committee NLP CAS  
Conference Date 2015-10-05 - 2015-10-06 
Place (in Japanese) (See Japanese page) 
Place (in English) Aster Plaza 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To NLP 
Conference Code 2015-10-NLP-CAS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Derivation of Multiplicative Update for Constrained Optimization Problems Related to NMF and Its Global Convergence Analysis 
Sub Title (in English)  
Keyword(1) nonnegative matrix factorization  
Keyword(2) multiplicative update  
Keyword(3) global convergence  
Keyword(4) generalized polynomial  
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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 2015-10-05 11:35:00 
Presentation Time 25 minutes 
Registration for NLP 
Paper # CAS2015-24, NLP2015-85 
Volume (vol) vol.115 
Number (no) no.239(CAS), no.240(NLP) 
Page pp.21-26 
#Pages 6 
Date of Issue 2015-09-28 (CAS, NLP) 

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