Presentation	2015-03-05 Effects of Numerical Errors against Sample Mahalanobis Distances Yasuyuki KOBAYASHI,
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Abstract(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) √> 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 √/>, 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.
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Keyword(in English)	Sample Mahalanobis Distance / Numerical Error / Condition Number / Round-off Error
Paper #	IBISML2014-90
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Conference Information
Committee	IBISML
Conference Date	2015/2/26(1days)
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Paper Information
Registration To	Information-Based Induction Sciences and Machine Learning (IBISML)
Language	JPN
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
1st Author's Name	Yasuyuki KOBAYASHI
1st Author's Affiliation	Faculty of Science and Engineering, Teikyo University()
Date	2015-03-05
Paper #	IBISML2014-90
Volume (vol)	vol.114
Number (no)	502
Page	pp.pp.-
#Pages	8
Date of Issue