| Presentation | 2017-01-20 A New Iterative Method for Nonnegative Matrix Factorization with Sparsity and Smoothness and Its Global Convergence Takumi Kimura, 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 an operation that decomposes a given nonnegative matrix into two nonnegative factor matrices. NMF is formulated as a constrained optimization problem that minimizes an error function under the constraint that all variables are nonnegative. The Hierarchical Alternating Least Squares (HALS) algorithm is one of the efficient computational methods for solving the NMF optimization problem. Cichocki et al. proposed a HALS algorithm that can control sparseness and smoothness of the obtained matrices by introducing regularization terms into Euclidean distance-based error function. However, if we apply their update rules, it is possible that the value of the error function increases. In this report, we propose a new HALS algorithm that decreases the value of the error function monotonically, and prove theoretically that the proposed update rule has the global convergence property. In addition, we verify the effectiveness of the proposed algorithm by conducting numerical experiments using synthetic data and real data obtained from facial images. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | nonnegative matrix factorization / hierarchical alternating least squares method / Euclidean distance / global convergence / sparseness / smoothness |
| Paper # | IT2016-93,SIP2016-131,RCS2016-283 |
| Date of Issue | 2017-01-12 (IT, SIP, RCS) |
| Conference Information | |
| Committee | IT / SIP / RCS |
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| Conference Date | 2017/1/19(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Osaka City Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Signal Processing for Wireless Communications, Learning, Mathematical Science, Communication Theory, etc. |
| Chair | Masayoshi Ohashi(Fukuoka Univ.) / Makoto Nakashizuka(Chiba Inst. of Tech.) / Hidekazu Murata(Kyoto Univ.) |
| Vice Chair | Jun Muramatsu(NTT) / Masahiro Okuda(Univ. of Kitakyushu) / Shogo Muramatsu(Niigata Univ.) / Satoshi Denno(Okayama Univ.) / Yukitoshi Sanada(Keio Univ.) / Eisuke Fukuda(Fujitsu Labs.) |
| Secretary | Jun Muramatsu(Wakayama Univ.) / Masahiro Okuda(Yokohama College of Commerce) / Shogo Muramatsu(Ritsumeikan Univ.) / Satoshi Denno(Chiba Inst. of Tech.) / Yukitoshi Sanada(Toshiba) / Eisuke Fukuda(NTT DoCoMo) |
| Assistant | Mitsugu Iwamoto(Univ. of Electro-Comm.) / Osamu Watanabe(Takushoku Univ.) / Tetsuya Yamamoto(Panasonic) / Toshihiko Nishimura(Hokkaido Univ.) / Koichi Ishihara(NTT) / Kazushi Muraoka(NEC) / Shinsuke Ibi(Osaka Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Information Theory / Technical Committee on Signal Processing / Technical Committee on Radio Communication Systems |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A New Iterative Method for Nonnegative Matrix Factorization with Sparsity and Smoothness and Its Global Convergence |
| Sub Title (in English) | |
| Keyword(1) | nonnegative matrix factorization |
| Keyword(2) | hierarchical alternating least squares method |
| Keyword(3) | Euclidean distance |
| Keyword(4) | global convergence |
| Keyword(5) | sparseness |
| Keyword(6) | smoothness |
| 1st Author's Name | Takumi Kimura |
| 1st Author's Affiliation | Okayana University(Okayama Univ.) |
| 2nd Author's Name | Norikazu Takahashi |
| 2nd Author's Affiliation | Okayana University(Okayama Univ.) |
| Date | 2017-01-20 |
| Paper # | IT2016-93,SIP2016-131,RCS2016-283 |
| Volume (vol) | vol.116 |
| Number (no) | IT-394,SIP-395,RCS-396 |
| Page | pp.pp.273-278(IT), pp.273-278(SIP), pp.273-278(RCS), |
| #Pages | 6 |
| Date of Issue | 2017-01-12 (IT, SIP, RCS) |