Handling possibilistic labels in pattern classification using evidential reasoning
A category of learning problems in which the class membership of training patterns is assessed by an expert and encoded in the form of a possibility distribution is considered. Each example i thus consists in a feature vector x ' and a possibilistic label (u(1)(i),..., u(c)(i)), where u(k)(i) denotes the possibility of that example belonging to class k. This problem is tackled in the framework of Evidence Theory. The evidential distance-based classifier previously introduced by one of the authors is extended to handle possibilistic labeling of training data. Two approaches are proposed, based either on the transformation of each possibility distribution into a consonant belief function, or on the use of generalized belief structures with fuzzy focal elements. In each case, a belief function modeling the expert's beliefs concerning the class membership of each new pattern is obtained. This information may then be either interpreted by a human operator to support decision-making, or automatically processed to yield a final class assignment through the computation of pignistic probabilities. Experiments with synthetic and real data demonstrate the ability of both classification schemes to make effective use of possibilistic labels as training information. (C) 2001 Elsevier Science B.V. All rights reserved.
evidence theory belief functions pattern recognition fuzzy statistics and data analysis possibility theory