| Presentation | 2011-05-19 Property of optimal sampling for one dimensional reduction by hyperplane fitting Jun FUJIKI, Shotaro AKAHO, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In this paper, N-1-dimensional hyperplane fitting for N-dimensional data is investigated. Firstly, the method that minimizes the k-th power deviation (least k-th power deviation) of L_p-distance is proposed and the concept of optimal sampling property, that is the global optimum passes through N data points for affine hyperplane fitting, and N-1 data points for linear hyperplane fitting, is introduced. Secondly, the condition that the method has the useful property, which is called optimal sampling property, is elucidated. On the other hand, it is proposed that least α-percentile of squares, that is the extension of least median of squares estimation. And the random sampling approximation of the least α-percentile of squares and the least k-th power deviation is proposed. The performances of these methods are evaluated by line extraction from images. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | hyperplane fitting / L_p-norm / least k-th power deviations / least α-percentile of squares / global optimum / optimal sampling property / combinatorial optimization / random sampling |
| Paper # | IE2011-20,PRMU2011-12,MI2011-12 |
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| Conference Information | |
| Committee | PRMU |
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| Conference Date | 2011/5/12(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Pattern Recognition and Media Understanding (PRMU) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Property of optimal sampling for one dimensional reduction by hyperplane fitting |
| Sub Title (in English) | |
| Keyword(1) | hyperplane fitting |
| Keyword(2) | L_p-norm |
| Keyword(3) | least k-th power deviations |
| Keyword(4) | least α-percentile of squares |
| Keyword(5) | global optimum |
| Keyword(6) | optimal sampling property |
| Keyword(7) | combinatorial optimization |
| Keyword(8) | random sampling |
| 1st Author's Name | Jun FUJIKI |
| 1st Author's Affiliation | The National Institute of Advanced Industrial Science and Technology (AIST)() |
| 2nd Author's Name | Shotaro AKAHO |
| 2nd Author's Affiliation | The National Institute of Advanced Industrial Science and Technology (AIST) |
| Date | 2011-05-19 |
| Paper # | IE2011-20,PRMU2011-12,MI2011-12 |
| Volume (vol) | vol.111 |
| Number (no) | 48 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |