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2 results on '"symmetric α-stable distributions"'

1. The Equivalency of Minimum Error Entropy Criterion and Minimum Dispersion Criterion for Symmetric Stable Signal Processing.

Author

Aimin Song and Tianshuang Qiu

Subjects
ENTROPY, ERROR analysis in mathematics, SIGNAL processing, ALGORITHMS, ESTIMATION theory
Abstract

The minimum error entropy (MEE) criterion in information theoretic learning is an efficient way to deal with non-Gaussian signal processing. And the minimum dispersion (MD) criterion has been widely applied in stable signal processing. In this letter, we show that there exists an equivalence between the MD criterion and the MEE criterion where symmetric α-stable (SαS) random variables are considered as the errors of the adaptive signal processing. As an application, we propose an algorithm with the MEE criterion for the time delay estimation (TDE) problem which was solved by the MD criterion. [ABSTRACT FROM AUTHOR]

Published
2010
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2. Continuous belief functions and α-stable distributions

Author

Fiche, A., Martin, A., Cexus, J. -C, Ali KHENCHAF, Lab-STICC_ENSTAB_MOM_PIM, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Lab-STICC_ENSTAB_CID_TOMS, and Cexus, Jean-Christophe

Subjects
pignistic probabilities, Belief functions, symmetric α-stable distributions, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, plausibility functions, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; The theory of belief functions has been formalized in continuous domain for pattern recognition. Some applications use assumption of Gaussian models. However, this assumption is reductive. Indeed, some data are not symmetric and present property of heavy tails. It is possible to solve these problems by using a class of distributions called α-stable distributions. Consequently, we present in this paper a way to calculate pignistic probabilities with plausibility functions where the knowledge of the sources of information is represented by symmetric α-stable distributions. To validate our approach, we compare our results in special case of Gaussian distributions with existing methods. To illustrate our work, we generate arbitrary distributions which represents speed of planes and take decisions. A comparison with a Bayesian approach is made to show the interest of the theory of belief functions.

Published
2010

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