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Paper Abstract and Keywords
Presentation 2024-10-18 14:50
An Extension of Multiplicative Update Rule for Nonnegative Matrix Factorization
Yuma Okazaki, Tsuyoshi Migita, Norikazu Takahashi (Okayama Univ.) CAS2024-57 NLP2024-87
Abstract (in Japanese) (See Japanese page) 
(in English) Nonnegative Matrix Factorization (NMF) is the process of decomposing a given nonnegative matrix into two nonnegative factor matrices. Since the NMF can extract nonnegative basic components from the given nonnegative data, it has been applied to various fields such as image processing, acoustic signal processing and network analysis. NMF is formulated as a problem of minimizing the error between the given nonnegative matrix and the product of two matrix variables under the constraint that the matrix variables are nonnegative. The Multiplicative Update Rule (MUR) is widely used as an efficient method for solving this problem. The main idea behind the MUR is to update the values of the variables by minimizing a strict convex function called the auxiliary function instead of the original objective function. However, the MUR fails to update when, for example, all entries in a row in one of the two matrix variables vanish. In this report, we extend the MUR so that it can update the values of the variables even in such cases, and show that the extended update rule has the global convergence property. It is expected that sparse solutions can be obtained using the new update rule.
Keyword (in Japanese) (See Japanese page) 
(in English) nonnegative matrix factorization / multiplicative update rule / global convergence / / / / /  
Reference Info. IEICE Tech. Rep., vol. 124, no. 208, NLP2024-87, pp. 150-155, Oct. 2024.
Paper # NLP2024-87 
Date of Issue 2024-10-10 (CAS, NLP) 
ISSN 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 2024-10-17 - 2024-10-18 
Place (in Japanese) (See Japanese page) 
Place (in English) Information Center, Tottori University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Nonlinear Problems, Circuits and Systems, etc. 
Paper Information
Registration To NLP 
Conference Code 2024-10-NLP-CAS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) An Extension of Multiplicative Update Rule for Nonnegative Matrix Factorization 
Sub Title (in English)  
Keyword(1) nonnegative matrix factorization  
Keyword(2) multiplicative update rule  
Keyword(3) global convergence  
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1st Author's Name Yuma Okazaki  
1st Author's Affiliation Okayama University (Okayama Univ.)
2nd Author's Name Tsuyoshi Migita  
2nd Author's Affiliation Okayama University (Okayama Univ.)
3rd Author's Name Norikazu Takahashi  
3rd Author's Affiliation Okayama University (Okayama Univ.)
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Speaker Author-1 
Date Time 2024-10-18 14:50:00 
Presentation Time 20 minutes 
Registration for NLP 
Paper # CAS2024-57, NLP2024-87 
Volume (vol) vol.124 
Number (no) no.207(CAS), no.208(NLP) 
Page pp.150-155 
#Pages 6 
Date of Issue 2024-10-10 (CAS, NLP) 

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