| Presentation | 2013-09-02 A Proposal of Simple Correcting Scheme for Sample Mahalanobis Distances using Delta Method Yasuyuki Kobayashi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In statistical machine learning technology, it is difficult to ignore errors between sample Mahalanobis distances estimated by learning samples and the population Mahalanobis distances. The errors result from not only estimation errors of eigen values but also those of eigenvectors from the covariance matrix of the learning samples. A correcting scheme from the sample Mahalanobis distances considering with the errors of the eigenvectors is not easy to execute. This report analyzed the expectation of the sample Mahalanobis distances by the Delta method, and proposed a simple correcting scheme by the Delta method from the sample Mahalanobis distances to the population Mahalanobis distances only with both the sample and the estimated population eigen values of the sample covariance matrix of the learning samples, but not with correction of the eigenvectors. This report also showed the effectiveness of the proposed correcting scheme to investigate the expectations, variances and distributions of the corrected sample Mahalanobis distances by simulation. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Machine Learning / Mahalanobis Distance / Delta Method / Eigenvalues of Covariance Matrix |
| Paper # | PRMU2013-37,IBISML2013-17 |
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| Conference Information | |
| Committee | PRMU |
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| Conference Date | 2013/8/26(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) | A Proposal of Simple Correcting Scheme for Sample Mahalanobis Distances using Delta Method |
| Sub Title (in English) | |
| Keyword(1) | Machine Learning |
| Keyword(2) | Mahalanobis Distance |
| Keyword(3) | Delta Method |
| Keyword(4) | Eigenvalues of Covariance Matrix |
| 1st Author's Name | Yasuyuki Kobayashi |
| 1st Author's Affiliation | Faculty of Science and Engineering, Teikyo University() |
| Date | 2013-09-02 |
| Paper # | PRMU2013-37,IBISML2013-17 |
| Volume (vol) | vol.113 |
| Number (no) | 196 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |