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Paper Abstract and Keywords
Presentation 2015-03-05 16:45
Effects of Numerical Errors against Sample Mahalanobis Distances
Yasuyuki Kobayashi (Teikyo Univ.) IBISML2014-90
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
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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. (No. 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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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
Date Time 2015-03-05 16:45:00 
Presentation Time 30 
Registration for IBISML 
Paper # IEICE-IBISML2014-90 
Volume (vol) IEICE-114 
Number (no) no.502 
Page pp.39-46 
#Pages IEICE-8 
Date of Issue IEICE-IBISML-2015-02-26 


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