| Presentation | 2021-06-28 Modification of Optimization Problem in Randomized NMF and Design of Optimization Method based on HALS Algorithm Takao Masuda, Tsuyoshi Migita, Norikazu Takahashi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(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) |
| Keyword(in English) | nonnegative matrix factorization / hierarchical alternating least squares algorithm / randomized NMF / global convergence |
| Paper # | NC2021-4,IBISML2021-4 |
| Date of Issue | 2021-06-21 (NC, IBISML) |
| Conference Information | |
| Committee | NC / IBISML / IPSJ-BIO / IPSJ-MPS |
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| Conference Date | 2021/6/28(3days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Rieko Osu(Waseda Univ.) / Ichiro Takeuchi(Nagoya Inst. of Tech.) / 倉田 博之(九工大) / 関嶋 政和(東工大) |
| Vice Chair | Hiroshi Yamakawa(Univ of Tokyo) / Masashi Sugiyama(Univ. of Tokyo) |
| Secretary | Hiroshi Yamakawa(ATR) / Masashi Sugiyama(NICT) / (Univ. of Tokyo) / (AIST) |
| Assistant | Nobuhiko Wagatsuma(Toho Univ.) / Tomoki Kurikawa(KMU) / Tomoharu Iwata(NTT) / Atsuyoshi Nakamura(Hokkaido Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Neurocomputing / Technical Committee on Infomation-Based Induction Sciences and Machine Learning / Special Interest Group on Bioinformatics and Genomics / Special Interest Group on Mathematical Modeling and Problem Solving |
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| Language | JPN |
| 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 |
| 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.) |
| Date | 2021-06-28 |
| Paper # | NC2021-4,IBISML2021-4 |
| Volume (vol) | vol.121 |
| Number (no) | NC-79,IBISML-80 |
| Page | pp.pp.23-30(NC), pp.23-30(IBISML), |
| #Pages | 8 |
| Date of Issue | 2021-06-21 (NC, IBISML) |