Classification using belief functions: Relationship between case-based and model-based approaches

The transferable belief model (TBM) is a model to represent quantified uncertainties based on belief functions, unrelated to any underlying probability model. In this framework, two main approaches to pattern classification have been developed: the TBM model-based classifier, relying on the general Bayesian theorem (GBT), and the TBM case-based classifier, built on the concept of similarity of a pattern to be classified with training patterns. Until now, these two methods seemed unrelated, and their connection with standard classification methods was unclear. This paper shows that both methods actually proceed from the same underlying principle, i.e., the GBT, and that they essentially differ by the nature of the assumed available information. This paper also shows that both methods collapse to a kernel rule in the case of precise and categorical learning data and for certain initial assumptions, and a simple relationship between basic belief assignments produced by the two methods is exhibited in a special case. These results shed new light on the issues of classification and supervised learning in the TBM. They also suggest new research directions and may help users in selecting the most appropriate method for each particular application, depending on the nature of the information at hand.