A Family of Bounded Divergence Measures Based on The Bhattacharyya Coefficient

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dc.contributor.author Jolad, Shivakumar
dc.contributor.author Roman, Ahmed
dc.contributor.author Shastry, Mahesh C.
dc.contributor.author Basu, Ayanendranath
dc.date.accessioned 2014-03-24T18:25:21Z
dc.date.available 2014-03-24T18:25:21Z
dc.date.issued 2014-09
dc.identifier.citation Jolad, Shivakumar et al., “A family of bounded divergence measures based on the Bhattacharyya coefficient”, arXiv, Cornell University Library, DOI: http://arxiv.org/abs/1201.0418, Jan. 2012. en_US
dc.identifier.issn arXiv:1201.0418
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/984
dc.description.abstract Divergence measures are widely used in various applications of pattern recognition, signal processing and statistical applications. In this paper, we introduce a new one parameter family of divergence measures, called bounded Bhattacharyya distance (BBD) measures, for quantifying the dissimilarity between probability distributions. These measures are bounded, symmetric and positive semi-definite. Unlike the Kullback-Leibler divergence, BBD measures do not require probability density functions to be absolutely continuous with respect to each other. In the asymptotic limit, BBD measure approach squared Hellinger distance. A generalized BBD measure for multiple distributions is also introduced. We prove an extension of a theorem of Bradt and Karlin for BBD relating Bayes error probability and Divergence ranking. We show that BBD belongs to the class of generalized Csiszar f-divergence and derive some properties such as curvature and relation to Fisher's Information. For distributions with vector valued parameters, the curvature matrix can be used to obtain the Rao geodesic distance. We also derive certain inequalities between BBD and well known measures such as Hellinger and Jensen-Shannon divergence. Bounds on the Bayesian error probability are established with BBD measure. en_US
dc.description.statementofresponsibility by Shivakumar Jolad et al.,
dc.description.statementofresponsibility by Shivakumar Jolad et al
dc.language.iso en en_US
dc.publisher arXiv, Cornell University Library en_US
dc.subject Bhattacharyya distance en_US
dc.subject Divergence measures en_US
dc.subject Pattern recognition en_US
dc.subject Signal classification en_US
dc.subject Signal detection en_US
dc.title A Family of Bounded Divergence Measures Based on The Bhattacharyya Coefficient en_US
dc.type Preprint

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