| Presentation | 2012-11-07 Clustering Method based on Global Optimization of Quadratic Forms Shunsuke HIROSE, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | This paper addresses the issue of constructing a clustering formulation by which we can derive a global optimum including parameter values. When dealing with clustering problems, it is difficult to formulate them as global optimization. When we formulate clustering problems, where we derive multiple cluster indicators, as eigen value problem like Spectral Clustering, we face a difficulty that negative probabilities appear. This is because components of eigen vectors have not fixed sign. Thus it is necessary to conduct post processing for suppressing the negetive components. Due to the additional processing, final results are not global optimum though the solutions without processing are global optimum. On the other hand, it is possible to construct convex clustering formulations if we assume some probability distibutions. However formulations with probability distribution assumption are not very effective. This is because clustering results strongly depend on the assumed distributions. In this paper, we propose a clustering method, by which the above mentioned difficulties can be avoided. The key ideas are as follows. First, we do not assume any distributions. Second, we adopt information maximization criterion. Third, we formulate a clustering problem as a combination of eigen value problem and convex quadratic programming. In the eigen value problem, we do not recognize eigen vectors as probalities but recognize them as probability amplitude. It is defined that the square of probability amplitude is equal to probability. By adopting probability amplitudes, we can avoid the negative probabilities and thus we can construct global optimization formulation. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | clusteirng / global optimization / eigen value problem / probability amplitude / quadratic form / information maximization |
| Paper # | IBISML2012-41 |
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| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2012/10/31(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 | Information-Based Induction Sciences and Machine Learning (IBISML) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Clustering Method based on Global Optimization of Quadratic Forms |
| Sub Title (in English) | |
| Keyword(1) | clusteirng |
| Keyword(2) | global optimization |
| Keyword(3) | eigen value problem |
| Keyword(4) | probability amplitude |
| Keyword(5) | quadratic form |
| Keyword(6) | information maximization |
| 1st Author's Name | Shunsuke HIROSE |
| 1st Author's Affiliation | Consulting Services Department, SAS Institute Japan Ltd.() |
| Date | 2012-11-07 |
| Paper # | IBISML2012-41 |
| Volume (vol) | vol.112 |
| Number (no) | 279 |
| Page | pp.pp.- |
| #Pages | 6 |
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