Evidential Matrix Metrics as Distances Between Meta-Data Dependent Bodies of Evidence

Mehena Loudahi (1) , John Klein (1) , Jean-Marc Vannobel (1) , Olivier Colot (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

As part of the theory of belief functions, we address the problem of ap-praising the similarity between bodies of evidence in a relevant way using metrics. Such metrics are called evidential distances and must be com-puted from mathematical objects depicting the information inside bodies of evidence. Specialization matrices are such objects and, therefore, an evidential distance can be obtained by computing the norm of the differ-ence of these matrices. Any matrix norm can be thus used to define a full metric. In this article, we show that other matrices can be used to obtain new evidential distances. These are the α-specialization and α-generalization matrices and are closely related to the α-junctive combination rules. We prove that any L 1 norm-based distance thus defined is consistent with its corresponding α-junction. If α > 0, these distances have in addition relevant variations induced by the poset structure of the belief function domain. Furthermore, α-junctions are meta-data dependent combination rules. The meta-data involved in α-junctions deals with the truthfulness of information sources. Consequently, the behavior of such evidential distances is analyzed in situations involving uncertain or partial meta-knowledge about information source truthfulness.

Mots clés: Index terms— Theory of belief functions; information source meta-datakeywords; com-bination rules; evidence theory; distance

Domaines: Analyse de données, Statistiques et Probabilités [physics.data-an]

Mehena Loudahi, John Klein, Jean-Marc Vannobel, Olivier Colot. Evidential Matrix Metrics as Distances Between Meta-Data Dependent Bodies of Evidence. IEEE transactions on systems, man, and cybernetics, 2016, 46 (1), pp.109 - 122. ⟨10.1109/TCYB.2015.2395877⟩. ⟨hal-01115637⟩