| Presentation | 2014-11-17 Approximate Models of Probability Distributions for Principal Components of Sample Mahalanobis Distances : About Each Element and Partial Sum of Sample Mahalanobis Distances Yasuyuki KOBAYASHI, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Probability distributions of the principal components and their partial sum, into which a sample Mahalanobis distance is decomposed by the eigenvalues and eigenvectors of the sample covariance matrix, are said to follow F distributions. However, the distributions do not follow F distributions when the number of the learning sample is small. This report has proposed approximate models of the distributions with x^2 or gamma distributions by analysis of the delta method in mathematical statistics, and has obtained more coincident results with the approximate models than with F distributions by numerical experiments. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Mahalanobis distance / principal components / partial sum / probability distribution / approximate models |
| Paper # | IBISML2014-37 |
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| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2014/11/10(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| 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) | Approximate Models of Probability Distributions for Principal Components of Sample Mahalanobis Distances : About Each Element and Partial Sum of Sample Mahalanobis Distances |
| Sub Title (in English) | |
| Keyword(1) | Mahalanobis distance |
| Keyword(2) | principal components |
| Keyword(3) | partial sum |
| Keyword(4) | probability distribution |
| Keyword(5) | approximate models |
| 1st Author's Name | Yasuyuki KOBAYASHI |
| 1st Author's Affiliation | Faculty of Science and Engineering, Teikyo University() |
| Date | 2014-11-17 |
| Paper # | IBISML2014-37 |
| Volume (vol) | vol.114 |
| Number (no) | 306 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |