| Presentation | 2014-07-11 Derivation of New Update Rules based on KL, γ, Renyi Divergences for Nonnegative Matrix Factorization Masato SEKI, Norikazu TAKAHASHI, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Three new update rules based on Kullback-Leibler divergence, γ-divergence and Renyi divergence for nonnegative matrix factorization are presented in this report. Multiplicative update rules based on these divergences have already been proposed by Yang and Oja. However, their error functions have a common problem that we can increase the values of variables as much as we want while keeping the value of the error function fixed. In addition, the global convergence of their multiplicative update rules is not guaranteed. In order to solve these problems, we add a penalty term to each of the original error functions, and derive three new update rules based on the method of Yang and Oja and the one of Gillis and Glineur. We also prove that the new update rules have the boundedness property which means that any sequence of solutions generated by the new update rules is contained in a bounded region. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | nonnegative matrix factorization / multiplicative update / boundedness / global convergence |
| Paper # | CAS2014-47,VLD2014-56,SIP2014-68,MSS2014-47,SIS2014-47 |
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| Committee | MSS |
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| Conference Date | 2014/7/2(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Registration To | Mathematical Systems Science and its applications(MSS) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Derivation of New Update Rules based on KL, γ, Renyi Divergences for Nonnegative Matrix Factorization |
| Sub Title (in English) | |
| Keyword(1) | nonnegative matrix factorization |
| Keyword(2) | multiplicative update |
| Keyword(3) | boundedness |
| Keyword(4) | global convergence |
| 1st Author's Name | Masato SEKI |
| 1st Author's Affiliation | Graduate School of Natural Science and Technology, Okayama University() |
| 2nd Author's Name | Norikazu TAKAHASHI |
| 2nd Author's Affiliation | Graduate School of Natural Science and Technology, Okayama University |
| Date | 2014-07-11 |
| Paper # | CAS2014-47,VLD2014-56,SIP2014-68,MSS2014-47,SIS2014-47 |
| Volume (vol) | vol.114 |
| Number (no) | 125 |
| Page | pp.pp.- |
| #Pages | 6 |
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