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Paper Abstract and Keywords
Presentation 2021-06-28 14:15
Modification of Optimization Problem in Randomized NMF and Design of Optimization Method based on HALS Algorithm
Takao Masuda, Tsuyoshi Migita, Norikazu Takahashi (Okayama Univ.) NC2021-4 IBISML2021-4
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.
Recently, randomized NMF has been proposed as an approach to fast NMF of large nonnegative matrices. The main idea of this approach is to perform NMF after reducing the dimensionality of the given nonnegative matrix by multiplying it by a random matrix. Since randomized NMF is formulated as a constrained optimization problem which is slightly different from the one for original NMF, it is necessary to develop suitable algorithms for solving it. However, the conventional algorithm has a serious drawback that the constraints of the optimization problem are not satisfied. Hence there is no guarantee that a feasible solution can be obtained. In addition, the convergence of the algorithm has not been analyzed. In this report, in order to overcome the drawback, we propose to modify the optimization problem slightly and design an algorithm based on the hierarchical alternating least squares method to solve the modified optimization problem. We also prove the global convergence of the designed algorithm.
Keyword (in Japanese) (See Japanese page) 
(in English) nonnegative matrix factorization / hierarchical alternating least squares algorithm / randomized NMF / global convergence / / / /  
Reference Info. IEICE Tech. Rep., vol. 121, no. 80, IBISML2021-4, pp. 23-30, June 2021.
Paper # IBISML2021-4 
Date of Issue 2021-06-21 (NC, IBISML) 
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)
Download PDF NC2021-4 IBISML2021-4

Conference Information
Committee NC IBISML IPSJ-BIO IPSJ-MPS  
Conference Date 2021-06-28 - 2021-06-30 
Place (in Japanese) (See Japanese page) 
Place (in English) Online 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To IBISML 
Conference Code 2021-06-NC-IBISML-BIO-MPS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Modification of Optimization Problem in Randomized NMF and Design of Optimization Method based on HALS Algorithm 
Sub Title (in English)  
Keyword(1) nonnegative matrix factorization  
Keyword(2) hierarchical alternating least squares algorithm  
Keyword(3) randomized NMF  
Keyword(4) global convergence  
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1st Author's Name Takao Masuda  
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 2021-06-28 14:15:00 
Presentation Time 25 minutes 
Registration for IBISML 
Paper # NC2021-4, IBISML2021-4 
Volume (vol) vol.121 
Number (no) no.79(NC), no.80(IBISML) 
Page pp.23-30 
#Pages 8 
Date of Issue 2021-06-21 (NC, IBISML) 

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