| Presentation | 2017-07-13 A Newton-Type Algorithm for Nonnegative Matrix Factorization with Alpha-Divergence Satoshi Nakatsu, Norikazu Takahashi, |
|---|---|
| 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. In this report we propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | nonnegative matrix factorization / alpha-divergence / optimization problem / Newton's method / global convergence |
| Paper # | NLP2017-31 |
| Date of Issue | 2017-07-06 (NLP) |
| Conference Information | |
| Committee | NLP |
|---|---|
| Conference Date | 2017/7/13(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Miyako Island Marine Terminal |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | etc. |
| Chair | Masaharu Adachi(Tokyo Denki Univ.) |
| Vice Chair | Norikazu Takahashi(Okayama Univ.) |
| Secretary | Norikazu Takahashi(Nagaoka Univ. of Tech.) |
| Assistant | Toshihiro Tachibana(Shonan Inst. of Tech.) / Masayuki Kimura(Kyoto Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Nonlinear Problems |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A Newton-Type Algorithm for Nonnegative Matrix Factorization with Alpha-Divergence |
| Sub Title (in English) | |
| Keyword(1) | nonnegative matrix factorization |
| Keyword(2) | alpha-divergence |
| Keyword(3) | optimization problem |
| Keyword(4) | Newton's method |
| Keyword(5) | global convergence |
| 1st Author's Name | Satoshi Nakatsu |
| 1st Author's Affiliation | Okayama University(Okayama Univ.) |
| 2nd Author's Name | Norikazu Takahashi |
| 2nd Author's Affiliation | Okayama University(Okayama Univ.) |
| Date | 2017-07-13 |
| Paper # | NLP2017-31 |
| Volume (vol) | vol.117 |
| Number (no) | NLP-121 |
| Page | pp.pp.17-22(NLP), |
| #Pages | 6 |
| Date of Issue | 2017-07-06 (NLP) |