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Belief function theory on the continuous space with an application to model based classification

par Ristic, Branko;Smets, Philippe
Référence Modern Information Processing, Elsevier, page (11-24)
Publication Publié, 2006

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Résumé :

This chapter presents a theoretical framework of the belief function theory in the continuous domain where the frame of discernment is the real axis R (or its segment). When the probabilistic description of observations in the continuous domain is incomplete, it is represented by the pignistic probability density. When the pignistic density is unimodal, the focal sets of the least committed belief function, which corresponds to this density, form a line in R2. This greatly simplifies the relationships between the basic belief density, pignistic density, and the plausibility function. The theory can be applied to the model-based target classification where observations of target speed and acceleration (in the continuous domain) are used as a feature. The classifier based on the belief function theory appears to be very simple to implement and produces the results that are arguably more meaningful than those obtained using the Bayesian classifier. For n-dimensional measurement space, it is required to extend the theory to the case where the frame is Rn. If features are independent, extending the theory to Rn would be manageable. If features are not independent, a transformation into new independent features would be first required. © 2006 Copyright © 2006 Elsevier B.V. All rights reserved..