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Fast computation of $L^p$ norm-based specialization distances between bodies of evidence

Mehena Loudahi 1 John Klein 1 Jean-Marc Vannobel 1 Olivier Colot 1
1 LAGIS-SI
LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : In a recent paper [1], 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 $L^1$ 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 $2^n \times 2^n$. 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 $L^p$ 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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Mehena Loudahi, John Klein, Jean-Marc Vannobel, Olivier Colot. Fast computation of $L^p$ norm-based specialization distances between bodies of evidence. thrid international conference on belief functions, Sep 2014, Oxford, United Kingdom. pp.422-431, ⟨10.1007/978-3-319-11191-9_46⟩. ⟨hal-01015330⟩

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