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Authors: Shivakumar Jolad 1 ; Ahmed Roman 2 ; Mahesh C. Shastry 3 ; Mihir Gadgil 4 and Ayanendranath Basu 5

Affiliations: 1 Indian Institute of Technology Gandhinagar, India ; 2 Virginia Tech, United States ; 3 Indian Institute of Science Education and Research Bhopal, India ; 4 Oregon Health & Science University, United States ; 5 Indian Statistical Institute, India

Keyword(s): Divergence Measures, Bhattacharyya Distance, Error Probability, F-divergence, Pattern Recognition, Signal Detection, Signal Classification.

Related Ontology Subjects/Areas/Topics: Applications ; Bayesian Models ; Classification ; Gaussian Processes ; Object Recognition ; Pattern Recognition ; Software Engineering ; Theory and Methods

Abstract: 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 and do not require absolute continuity. In the asymptotic limit, BBD measure approaches the 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 Information. For distributions with vector valued parameters, the curvature matrix is related to the Fisher-Rao metric. We derive certain inequalities between BBD and well known measures such as Hellinger and Jensen-Shannon divergence. We also derive bounds on the Bayesian error probability . We give an application of these measures to the problem of signal detection where we compare two monochromatic signals buried in white noise and differing in frequency and amplitude. (More)

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Paper citation in several formats:
Jolad, S.; Roman, A.; Shastry, M.; Gadgil, M. and Basu, A. (2016). A New Family of Bounded Divergence Measures and Application to Signal Detection. In Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - ICPRAM; ISBN 978-989-758-173-1; ISSN 2184-4313, SciTePress, pages 72-83. DOI: 10.5220/0005695200720083

@conference{icpram16,
author={Shivakumar Jolad. and Ahmed Roman. and Mahesh C. Shastry. and Mihir Gadgil. and Ayanendranath Basu.},
title={A New Family of Bounded Divergence Measures and Application to Signal Detection},
booktitle={Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - ICPRAM},
year={2016},
pages={72-83},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005695200720083},
isbn={978-989-758-173-1},
issn={2184-4313},
}

TY - CONF

JO - Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - ICPRAM
TI - A New Family of Bounded Divergence Measures and Application to Signal Detection
SN - 978-989-758-173-1
IS - 2184-4313
AU - Jolad, S.
AU - Roman, A.
AU - Shastry, M.
AU - Gadgil, M.
AU - Basu, A.
PY - 2016
SP - 72
EP - 83
DO - 10.5220/0005695200720083
PB - SciTePress