Kohonen's Map Approach for the Belief Mass Modeling

Imen Hammami (1, 2) , Grégoire Mercier (1, 2) , Atef Hamouda (3) , Jean Dezert (4)

1 Lab-STICC_TB_CID_TOMS
2 ITI - Département Image et Traitement Information
3 FST - Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis
4 ONERA - The French Aerospace Lab [Palaiseau]

In the framework of the evidence theory, several approaches for estimating belief functions are proposed. However, they generally suffer from the problem of masses attribution in case of compound hypotheses that lose much conceptual contribution of the theory. In this paper, an original method for estimating mass functions using Kohonen's map derived from the initial feature space and an initial classifier is proposed. Our approach allows a smart mass belief assignment, not only for simple hypotheses, but also for disjunctions and conjunctions of hypotheses. Thus, it can model at the same time ignorance, imprecision and paradox. The proposed method for basic belief assignment (BBA) is of interest for solving estimation mass functions problems where a large quantity of multi-variate data is available. Indeed, the use of Kohonen map simplifies the process of assigning mass functions. The proposed method has been compared to state-of-the art BBA technique on benchmark database and applied on remote sensing data for image classifi- cation purpose. Experimentation shows that our approach gives similar or better results than other methods presented in the literature so far, with an ability to handle large amount of data.

Mots clés: Evidence Theory; Mass belief assignment; Kohonen map

Domaines: Traitement du signal et de l'image [eess.SP]; Méthodologie [stat.ME]

Imen Hammami, Grégoire Mercier, Atef Hamouda, Jean Dezert. Kohonen's Map Approach for the Belief Mass Modeling. IEEE Transactions on Neural Networks and Learning Systems, 2015, 27 (10), pp.2060 - 2071. ⟨10.1109/TNNLS.2015.2480772⟩. ⟨hal-01865183⟩