| Presentation | 2015-11-26 [Poster Presentation] Approximate Distribution Followed by A Principal Component Term Corresponding with the Population Eigenvalue of zero value in the Q Statistic Yasuyuki Kobayashi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The Mahalanobis distance requires all the population eigenvalues of the population covariance matrix larger than zero. However, some population eigenvalues of the population covariance matrix from the probability distribution followed by learning samples may contain zero value. Including this case, when the eigenvalues of the sample covariance are extremely small, it is said that the Q statistic is adequate to analyze with the Mahalanobis distance. However, the existing approximate distribution models followed by the Q statistic cannot handle the case including the population eigenvalues of zero value. Therefore, this report has proposed the approximate probability distribution models followed by the sample eigenvalue and the principal component of the Q statistic corresponding with the population eigenvalue of zero value, considering the effect of numerical errors theoretically. The numerical experiment has shown that the empirical distributions obtained by Monte Carlo simulation coincides with the proposed approximate distribution models on the whole. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Mahalanobis Distance / Q Statistic / Principal Component / Probability Distribution / Approximate Model |
| Paper # | IBISML2015-52 |
| Date of Issue | 2015-11-19 (IBISML) |
| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2015/11/25(3days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Epochal Tsukuba |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Information-Based Induction Science Workshop (IBIS2015) |
| Chair | Takashi Washio(Osaka Univ.) |
| Vice Chair | Kenji Fukumizu(ISM) / Masashi Sugiyama(Tokyo Inst. of Tech.) |
| Secretary | Kenji Fukumizu(ISM) / Masashi Sugiyama(Kyoto Univ.) |
| Assistant | Koji Tsuda(Univ. of Tokyo) / Hisashi Kashima(Kyoto Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Infomation-Based Induction Sciences and Machine Learning |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | [Poster Presentation] Approximate Distribution Followed by A Principal Component Term Corresponding with the Population Eigenvalue of zero value in the Q Statistic |
| Sub Title (in English) | |
| Keyword(1) | Mahalanobis Distance |
| Keyword(2) | Q Statistic |
| Keyword(3) | Principal Component |
| Keyword(4) | Probability Distribution |
| Keyword(5) | Approximate Model |
| 1st Author's Name | Yasuyuki Kobayashi |
| 1st Author's Affiliation | Teikyo University(Teikyo Univ.) |
| Date | 2015-11-26 |
| Paper # | IBISML2015-52 |
| Volume (vol) | vol.115 |
| Number (no) | IBISML-323 |
| Page | pp.pp.1-7(IBISML), |
| #Pages | 7 |
| Date of Issue | 2015-11-19 (IBISML) |