The Bhattacharyya metric as an absolute similarity measure for frequency coded data

Frank J. Aherne; Neil A. Thacker; Peter I Rockett

Kybernetika (1998)

  • Volume: 34, Issue: 4, page [363]-368
  • ISSN: 0023-5954

Abstract

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This paper highlights advantageous properties of the Bhattacharyya metric over the chi-squared statistic for comparing frequency distributed data. The original interpretation of the Bhattacharyya metric as a geometric similarity measure is reviewed and it is pointed out that this derivation is independent of the use of the Bhattacharyya measure as an upper bound on the probability of misclassification in a two-class problem. The affinity between the Bhattacharyya and Matusita measures is described and we suggest use of the Bhattacharyya measure for comparing histogram data. We explain how the chi- squared statistic compensates for the implicit assumption of a Euclidean distance measure being the shortest path between two points in high dimensional space. By using the square-root transformation the Bhattacharyya metric requires no such standardization and by its multiplicative nature has no singularity problems (unlike those caused by the denominator of the chi- squared statistic) with zero count-data.

How to cite

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Aherne, Frank J., Thacker, Neil A., and Rockett, Peter I. "The Bhattacharyya metric as an absolute similarity measure for frequency coded data." Kybernetika 34.4 (1998): [363]-368. <http://eudml.org/doc/33362>.

@article{Aherne1998,
abstract = {This paper highlights advantageous properties of the Bhattacharyya metric over the chi-squared statistic for comparing frequency distributed data. The original interpretation of the Bhattacharyya metric as a geometric similarity measure is reviewed and it is pointed out that this derivation is independent of the use of the Bhattacharyya measure as an upper bound on the probability of misclassification in a two-class problem. The affinity between the Bhattacharyya and Matusita measures is described and we suggest use of the Bhattacharyya measure for comparing histogram data. We explain how the chi- squared statistic compensates for the implicit assumption of a Euclidean distance measure being the shortest path between two points in high dimensional space. By using the square-root transformation the Bhattacharyya metric requires no such standardization and by its multiplicative nature has no singularity problems (unlike those caused by the denominator of the chi- squared statistic) with zero count-data.},
author = {Aherne, Frank J., Thacker, Neil A., Rockett, Peter I},
journal = {Kybernetika},
keywords = {chi-square statistic},
language = {eng},
number = {4},
pages = {[363]-368},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The Bhattacharyya metric as an absolute similarity measure for frequency coded data},
url = {http://eudml.org/doc/33362},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Aherne, Frank J.
AU - Thacker, Neil A.
AU - Rockett, Peter I
TI - The Bhattacharyya metric as an absolute similarity measure for frequency coded data
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 4
SP - [363]
EP - 368
AB - This paper highlights advantageous properties of the Bhattacharyya metric over the chi-squared statistic for comparing frequency distributed data. The original interpretation of the Bhattacharyya metric as a geometric similarity measure is reviewed and it is pointed out that this derivation is independent of the use of the Bhattacharyya measure as an upper bound on the probability of misclassification in a two-class problem. The affinity between the Bhattacharyya and Matusita measures is described and we suggest use of the Bhattacharyya measure for comparing histogram data. We explain how the chi- squared statistic compensates for the implicit assumption of a Euclidean distance measure being the shortest path between two points in high dimensional space. By using the square-root transformation the Bhattacharyya metric requires no such standardization and by its multiplicative nature has no singularity problems (unlike those caused by the denominator of the chi- squared statistic) with zero count-data.
LA - eng
KW - chi-square statistic
UR - http://eudml.org/doc/33362
ER -

References

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  1. Aherne F. J., Thacker N. A., Rockett P. I., Optimal pairwise geometric histograms, In: Proc. 8th British Machine Vision Conf., Colchester 1997, pp. 480–490 (1997) 
  2. Bhattacharyya A., On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc. 35 (1943), 99–110 (1943) Zbl0063.00364MR0010358
  3. Christensen R., Linear Models for Multivariate Time Series and Spatial Data, Springer–Verlag, New York 1991 Zbl0717.62079MR1081535
  4. Fukanaga K., Introduction to Statistical Pattern Recognition, Second edition. Academic Press, New York 1990 MR1075415
  5. Matusita K., 10.1214/aoms/1177728422, Ann. Math. Statist. 26 (1955), 631–641 (1955) MR0073899DOI10.1214/aoms/1177728422
  6. Thacker N. A., Abraham, I., Courtney P. G., 10.1016/S0893-6080(96)00074-3, Neural Network J. 10 (1997), 2, 315–326 (1997) DOI10.1016/S0893-6080(96)00074-3

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