Abstract
The theory of belief functions in discrete domain has been employed with success for pattern recognition. However, the Bayesian approach performs well provided that once the probability density functions are well estimated. Recently, the theory of belief functions has been more and more developed to the continuous case. In this paper, we compare results obtained by a Bayesian approach and a method based on continuous belief functions to characterize seabed sediments. The probability density functions of each feature of seabed sediments are unimodal and estimated from a Gaussian model and compared with an α-stable model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Caron, F., Ristic, B., Duflos, E., Vanheeghe, P.: Least Committed basic belief density induced by a multivariate Gaussian pdf. International Journal of Approximate Reasoning 48(2), 419–436 (2008)
Caughey, D., Prager, B., Klymak, J.: Sea bottom classification from echo sounding data. Quester Tangent Corporation, Marine Technology Center, British Columbia, V8L 3S1, Canada (1994)
Delmotte, F., Smets, P.: Target identification based on the transferable belief model interpretation of Dempster–Shafer model. IEEE Transactions on Systems, Man, and Cybernetics 34(4), 457–471 (2004)
Dempster, A.: Upper and Lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38, 325–339 (1967)
Denœux, T.: Extending stochastic ordering to belief functions on the real line. Information Science 179(9), 1362–1376 (2009)
Doré, P.E., Martin, A., Khenchaf, A.: Constructing of a consonant belief function induced by a multimodal probability density function. In: COGnitive Systems with Interactive Sensors (COGIS 2009), Paris (2009)
Fiche, A., Martin, A., Cexus, J.C., Khenchaf, A.: Continuous belief functions and α-stable distributions. In: International Conference on Information Fusion, Edinburgh, United Kingdom (2010)
Koutrouvelis, I.A.: An iterative procedure for the estimation of the parameters of stable laws. Communications in Statistics-Simulation and Computation 10(1), 17–28 (1981)
Nolan, J.P.: Numerical calculation of stable densities and distribution functions. Communications in Statistics-Stochastic Models 13(4), 759–774 (1997)
Nolan, J.P.: Stable Distributions - Models for Heavy Tailed Data, ch. 1 (in progress, 2012), academic2.american.edu/~jpnolan
Ristic, B., Smets, P.: Belief function theory on the continuous space with an application to model based classification. In: Proceedings of Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU, pp. 4–9 (2004)
Ristic, B., Smets, P.: Target classification approach based on the belief function theory. IEEE Transactions on Aerospace and Electronic Systems 42(2), 574–583 (2005)
Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)
Smets, P.: Constructing the pignistic probability function in a context of uncertainty. Uncertainty in Artificial Intelligence 5, 29–39 (1990)
Smets, P.: Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate Reasoning 9(1), 1–35 (1993)
Smets, P.: Belief functions on real numbers. International Journal of Approximate Reasoning 40(3), 181–223 (2005)
Taqqu, M.S., Samorodnisky, G.: Stable non-gaussian random processes. Chapman and Hall (1994)
Zolotarev, V.M.: One-dimensional stable distributions. Translations of Mathematical Monographs, vol. 65. American Mathematical Society (1986); Translation from the original 1983 Russian edition
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fiche, A., Martin, A., Cexus, JC., Khenchaf, A. (2012). A Comparison between a Bayesian Approach and a Method Based on Continuous Belief Functions for Pattern Recognition. In: Denoeux, T., Masson, MH. (eds) Belief Functions: Theory and Applications. Advances in Intelligent and Soft Computing, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29461-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-29461-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29460-0
Online ISBN: 978-3-642-29461-7
eBook Packages: EngineeringEngineering (R0)