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Paper Abstract and Keywords
Presentation 2013-09-02 10:00
A proposal of simple correcting scheme for sample Mahalanobis distances using Delta method
Yasuyuki Kobayashi (Teikyo Univ.) PRMU2013-37 IBISML2013-17
Abstract (in Japanese) (See Japanese page) 
(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 eigenvalues 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 eigenvalues 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) 
(in English) Machine Learning / Mahalanobis Distance / Delta Method / Eigenvalues of Covariance Matrix / / / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 197, IBISML2013-17, pp. 25-30, Sept. 2013.
Paper # IBISML2013-17 
Date of Issue 2013-08-26 (PRMU, 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 PRMU2013-37 IBISML2013-17

Conference Information
Committee PRMU IBISML IPSJ-CVIM  
Conference Date 2013-09-02 - 2013-09-03 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
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Paper Information
Registration To IBISML 
Conference Code 2013-09-PRMU-IBISML-CVIM 
Language Japanese 
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  
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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 2013-09-02 10:00:00 
Presentation Time 30 minutes 
Registration for IBISML 
Paper # PRMU2013-37, IBISML2013-17 
Volume (vol) vol.113 
Number (no) no.196(PRMU), no.197(IBISML) 
Page pp.25-30 
#Pages 6 
Date of Issue 2013-08-26 (PRMU, IBISML) 

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