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Fast Computation of Lp Norm-Based Specialization Distances between Bodies of Evidence

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Belief Functions: Theory and Applications (BELIEF 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8764))

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Abstract

In a recent paper [12], we introduced a new family of evidential distances in the framework of belief functions. Using specialization matrices as a representation of bodies of evidence, an evidential distance can be obtained by computing the norm of the difference of these matrices. Any matrix norm can be thus used to define a full metric. In particular, it has been shown that the L1 norm-based specialization distance has nice properties. This distance takes into account the structure of focal elements and has a consistent behavior with respect to the conjunctive combination rule. However, if the frame of discernment on which the problem is defined has n elements, then a specialization matrix size is 2n ×2n. The straightforward formula for computing a specialization distance involves a matrix product which can be consequently highly time consuming. In this article, several faster computation methods are provided for Lp norm-based specialization distances. These methods are proposed for special kinds of mass functions as well as for the general case.

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Authors and Affiliations

  1. LAGIS UMR CNRS 8219, Lille1 University, avenue Carl Gauss, cité scientifique, 59650, Villeneuve d’Ascq, France

    Mehena Loudahi, John Klein, Jean-Marc Vannobel & Olivier Colot

Authors
  1. Mehena Loudahi
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  2. John Klein
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  3. Jean-Marc Vannobel
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  4. Olivier Colot
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Editor information

Editors and Affiliations

  1. Department of Computing and Communications Technologies, Oxford Brookes University, Wheatley Campus, OX33 1HX, Oxford, UK

    Fabio Cuzzolin

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© 2014 Springer International Publishing Switzerland

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Loudahi, M., Klein, J., Vannobel, JM., Colot, O. (2014). Fast Computation of Lp Norm-Based Specialization Distances between Bodies of Evidence. In: Cuzzolin, F. (eds) Belief Functions: Theory and Applications. BELIEF 2014. Lecture Notes in Computer Science(), vol 8764. Springer, Cham. https://doi.org/10.1007/978-3-319-11191-9_46

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  • DOI: https://doi.org/10.1007/978-3-319-11191-9_46

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11190-2

  • Online ISBN: 978-3-319-11191-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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