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| Presentation | 2015-03-05 16:45 Effects of Numerical Errors against Sample Mahalanobis Distances Yasuyuki Kobayashi (Teikyo Univ.)  IBISML2014-90 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | I have studied the detail conditions that the numerical errors of sample Mahalanobis distances (T^2=y^' S^(-1) y) of the sample covariance matrix S can be suppressed and have found the two following conditions by the theoretical analysis and numerical experiments. 1) √(l_min ) as the square root of the minimum eigenvalue of the matrix S should be larger than ε_A as the maximum numerical error of the eigenvalues, and 2) ||Δy||/||y|| as the relative numerical error of the vector y, should be smaller than √(l_min/l_max) , the inverse square root of the condition number of the matrix S. As a result, if the significant figure number of the real variables storing the vector y is larger than the significant figure number of the vector y itself, the significant figure number of the vector y itself determines the upper bound of the condition number of the matrix S. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | sample Mahalanobis distance / numerical error / condition number / round-off error / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 114, no. 502, IBISML2014-90, pp. 39-46, March 2015. | |
| Paper # | IBISML2014-90 | |
| Date of Issue | 2015-02-26 (IBISML) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | IBISML2014-90 |
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| Conference Information | |
| Committee | IBISML |
| Conference Date | 2015-03-05 - 2015-03-06 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kyoto University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Statistical mathematics, machine learning, data mining, and others |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2015-03-IBISML |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Effects of Numerical Errors against Sample Mahalanobis Distances |
| Sub Title (in English) | |
| Keyword(1) | sample Mahalanobis distance |
| Keyword(2) | numerical error |
| Keyword(3) | condition number |
| Keyword(4) | round-off error |
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| 1st Author's Name | Yasuyuki Kobayashi |
| 1st Author's Affiliation | Teikyo University (Teikyo Univ.) |
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| Speaker | Author-1 |
| Date Time | 2015-03-05 16:45:00 |
| Presentation Time | 30 minutes |
| Registration for | IBISML |
| Paper # | IBISML2014-90 |
| Volume (vol) | vol.114 |
| Number (no) | no.502 |
| Page | pp.39-46 |
| #Pages | 8 |
| Date of Issue | 2015-02-26 (IBISML) |
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