Likelihood-based vs. distance-based evidential classifiers

This paper presents and compares several evidential classifiers, i.e., classification rules based on the Dempster-Shafer theory of evidence. Three methods used in the majority of applications are compared, with emphasis on the techniques used to build belief functions from learning data. The methods are: the consonant method initially introduced by Shafer (1976) in the more general context of statistical inference, Appriou´s separable method (1998), and the distance-based classifier introduced by Denoeux. These models can be derived with two decisions rules, based on the minimization of, respectively, lower and pignistic expected loss. Simulations on synthetic data demonstrate the performance of these techniques and allow to compare the behavior of the proposed models