| Presentation | 2008-03-07 A Non-negative Matrix Factorization Based on Best Low-Rank Matrix Approximation Akira NIHEI, Takashi MATSUSHITA, Noriyuki TAKAHASHI, Isao YAMADA, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Given a non-negative matrix, the non-negative matrix factorization (NMF) is a problem to find a pair of smaller non-negative matrices, say factor matrices, of which multiplication well approximates the original matrix. The NMF attracts great attention because it is useful to obtain a compact representation of non-negative data. A most well-known method named "multiplicative update" was proposed by Lee and Seung. This method is designed to reduce monotonically the Frobenius norm of the approximation error, which unfortunately can not often reach a good approximation due to the nonconvexity of the cost function of a pair of matrices. In this report, we propose a pair of efficient algorithms for the NMF by introducing a reasonable search domain for candidates of each factor matrix. The proposed search domain for the left (right) factor matrix is defined as all nonnegative matrices of which column (row) space is restricted in the column (row) space of the reduced rank best approximation matrix of the original matrix, where the reduced rank best approximation matrix is obtained as the truncated singular value decomposition. Finally, by comparing with the multiplicative update, we verified that the proposed algorithms exhibit much better convergence performance. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Nonnegative matrix factorization / Singular value decomposition / Nonexpansive mapping |
| Paper # | CAS2007-155,SIP2007-230,CS2007-120 |
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| Committee | CS |
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| Conference Date | 2008/2/29(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Communication Systems (CS) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A Non-negative Matrix Factorization Based on Best Low-Rank Matrix Approximation |
| Sub Title (in English) | |
| Keyword(1) | Nonnegative matrix factorization |
| Keyword(2) | Singular value decomposition |
| Keyword(3) | Nonexpansive mapping |
| 1st Author's Name | Akira NIHEI |
| 1st Author's Affiliation | Dept. of Communications & Integrated Systems, Tokyo Institute of Technology() |
| 2nd Author's Name | Takashi MATSUSHITA |
| 2nd Author's Affiliation | Dept. of Communications & Integrated Systems, Tokyo Institute of Technology |
| 3rd Author's Name | Noriyuki TAKAHASHI |
| 3rd Author's Affiliation | Dept. of Communications & Integrated Systems, Tokyo Institute of Technology |
| 4th Author's Name | Isao YAMADA |
| 4th Author's Affiliation | Dept. of Communications & Integrated Systems, Tokyo Institute of Technology |
| Date | 2008-03-07 |
| Paper # | CAS2007-155,SIP2007-230,CS2007-120 |
| Volume (vol) | vol.107 |
| Number (no) | 531 |
| Page | pp.pp.- |
| #Pages | 4 |
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