IEICE TRANSACTIONS on Information
Effects of Numerical Errors on Sample Mahalanobis Distances
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Information Vol.E99-D No.5 pp.1337-1344
- Publication Date
- 2016/05/01
- Publicized
- 2016/02/12
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2015EDP7348
- Type of Manuscript
- PAPER
- Category
- Artificial Intelligence, Data Mining
Authors
Yasuyuki KOBAYASHI
Teikyo University
Keyword
Latest Issue
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Yasuyuki KOBAYASHI, "Effects of Numerical Errors on Sample Mahalanobis Distances" in IEICE TRANSACTIONS on Information,
vol. E99-D, no. 5, pp. 1337-1344, May 2016, doi: 10.1587/transinf.2015EDP7348.
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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2015EDP7348/_p
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@ARTICLE{e99-d_5_1337,
author={Yasuyuki KOBAYASHI, },
journal={IEICE TRANSACTIONS on Information},
title={Effects of Numerical Errors on Sample Mahalanobis Distances},
year={2016},
volume={E99-D},
number={5},
pages={1337-1344},
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.},
keywords={},
doi={10.1587/transinf.2015EDP7348},
ISSN={1745-1361},
month={May},}
Copy
TY - JOUR
TI - Effects of Numerical Errors on Sample Mahalanobis Distances
T2 - IEICE TRANSACTIONS on Information
SP - 1337
EP - 1344
AU - Yasuyuki KOBAYASHI
PY - 2016
DO - 10.1587/transinf.2015EDP7348
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E99-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 2016
AB - 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.
ER -
English
