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Paper Abstract and Keywords
Presentation 2023-03-17 14:30
Global Convergence Analysis of Distributed HALS Algorithm for Nonnegative Matrix Factorization
Keiju Hayashi, Tsuyoshi Migita, Norikazu Takahashi (Okayama Univ.) MSS2022-104 NLP2022-149
Abstract (in Japanese) (See Japanese page) 
(in English) As a fast computational method for Nonnegative Matrix Factorization (NMF),
the Hierarchical Alternating Least Squares (HALS) algorithm is widely known.
Recently, an algorithm for multiple agents communicating with each other to execute the HALS algorithm in a distributed manner was proposed. This algorithm enables us to perform NMF on large matrices that cannot be handled by a single agent. However, the average consensus algorithm used there requires each agent to store the entire history of the values of its variables until the complete average consensus is reached. This increases the memory usage and computational cost of each agent. In order to solve this problem, the authors proposed a distributed HALS algorithm using a simpler average consensus algorithm in which each agent does not have to store the entire history of the values. In this report, we prove that the proposed algorithm has the Zangwill's global convergence property if the number of iterations of the average consensus algorithm is properly set.
Keyword (in Japanese) (See Japanese page) 
(in English) nonnegative matrix factorization / hierarchical alternating least squares algorithm / distributed algorithm / average consensus / global convergence / / /  
Reference Info. IEICE Tech. Rep., vol. 122, no. 436, NLP2022-149, pp. 198-203, March 2023.
Paper # NLP2022-149 
Date of Issue 2023-03-08 (MSS, NLP) 
ISSN Online edition: ISSN 2432-6380
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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 MSS  
Conference Date 2023-03-15 - 2023-03-17 
Place (in Japanese) (See Japanese page) 
Place (in English)  
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Topics (in English)  
Paper Information
Registration To NLP 
Conference Code 2023-03-NLP-MSS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Global Convergence Analysis of Distributed HALS Algorithm for Nonnegative Matrix Factorization 
Sub Title (in English)  
Keyword(1) nonnegative matrix factorization  
Keyword(2) hierarchical alternating least squares algorithm  
Keyword(3) distributed algorithm  
Keyword(4) average consensus  
Keyword(5) global convergence  
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1st Author's Name Keiju Hayashi  
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 2023-03-17 14:30:00 
Presentation Time 20 minutes 
Registration for NLP 
Paper # MSS2022-104, NLP2022-149 
Volume (vol) vol.122 
Number (no) no.435(MSS), no.436(NLP) 
Page pp.198-203 
#Pages
Date of Issue 2023-03-08 (MSS, NLP) 


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