IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Regular Section
Effects of Numerical Errors on Sample Mahalanobis Distances
Yasuyuki KOBAYASHI
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2016 Volume E99.D Issue 5 Pages 1337-1344

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Abstract

The numerical error of a sample Mahalanobis distance (T2=y'S-1y) with sample covariance matrix S is investigated. It is found that in order to suppress the numerical error of T2, the following conditions need to be satisfied. First, the reciprocal square root of the condition number of S should be larger than the relative error of calculating floating-point real-number variables. The second proposed condition is based on the relative error of the observed sample vector y in T2. If the relative error of y is larger than the relative error of the real-number variables, the former governs the numerical error of T2. Numerical experiments are conducted to show that the numerical error of T2 can be suppressed if the two above-mentioned conditions are satisfied.

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© 2016 The Institute of Electronics, Information and Communication Engineers
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