DocumentCode :
2491181
Title :
Numerical analysis of Mahalanobis metric in vector space
Author :
Joken, Son ; Inoue, Naoya ; Yamashita, Yukihiko
Author_Institution :
IBM Global Services Japan, Tokyo
fYear :
2008
fDate :
8-11 Dec. 2008
Firstpage :
1
Lastpage :
4
Abstract :
The Mahalanobis metric was proposed by extending the Mahalanobis distance to provide a probabilistic distance for a non-normal distribution. The Mahalanobis metric equation is a nonlinear second order differential equation derived from the equation of geometrically local isotropic independence, which is proposed to define normal distributions in a manifold. In this paper we provide experimental results of calculating the Mahalanobis metric by the Newton-Raphson method. We add error to the original probability density function and calculate the Mahalanobis metric to investigate the effect of the error in a probability density function to the solution.
Keywords :
Newton-Raphson method; computational geometry; error statistics; nonlinear differential equations; statistical distributions; Mahalanobis distance; Mahalanobis metric equation; Newton-Raphson method; error statistics; geometrically local isotropic independence equation; nonlinear second order differential equation; nonnormal distribution; normal distribution; numerical analysis; probabilistic distance; probability density function; vector space; Covariance matrix; Differential equations; Euclidean distance; Extraterrestrial measurements; Gaussian distribution; Newton method; Nonlinear equations; Numerical analysis; Probability density function; Space technology;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Pattern Recognition, 2008. ICPR 2008. 19th International Conference on
Conference_Location :
Tampa, FL
ISSN :
1051-4651
Print_ISBN :
978-1-4244-2174-9
Electronic_ISBN :
1051-4651
Type :
conf
DOI :
10.1109/ICPR.2008.4761901
Filename :
4761901
Link To Document :
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