| Presentation | 2023-03-17 Global Convergence Analysis of Distributed HALS Algorithm for Nonnegative Matrix Factorization Keiju Hayashi, Tsuyoshi Migita, Norikazu Takahashi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(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) |
| Keyword(in English) | nonnegative matrix factorization / hierarchical alternating least squares algorithm / distributed algorithm / average consensus / global convergence |
| Paper # | MSS2022-104,NLP2022-149 |
| Date of Issue | 2023-03-08 (MSS, NLP) |
| Conference Information | |
| Committee | NLP / MSS |
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| Conference Date | 2023/3/15(3days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Akio Tsuneda(Kumamoto Univ.) / Atsuo Ozaki(Osaka Inst. of Tech.) |
| Vice Chair | Hiroyuki Torikai(Hosei Univ.) / Shingo Yamaguchi(Yamaguchi Univ.) |
| Secretary | Hiroyuki Torikai(Sojo Univ.) / Shingo Yamaguchi(Gifu Univ.) |
| Assistant | Yuichi Yokoi(Nagasaki Univ.) / Yoshikazu Yamanaka(Utsunomiya Univ.) / Masato Shirai(Shimane Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Nonlinear Problems / Technical Committee on Mathematical Systems Science and its Applications |
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| Language | JPN |
| 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 |
| 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.) |
| Date | 2023-03-17 |
| Paper # | MSS2022-104,NLP2022-149 |
| Volume (vol) | vol.122 |
| Number (no) | MSS-435,NLP-436 |
| Page | pp.pp.198-203(MSS), pp.198-203(NLP), |
| #Pages | 6 |
| Date of Issue | 2023-03-08 (MSS, NLP) |