12 NUMERICAL SYMBOLIC AND HYBRID SUPERVISED CLASSIFICATION METHODS

Supervised classification has already been the subject of numerous stu dies in the fields of Statistics, Pattern Recognition and Artificial I ntelligence under various appellations which include discriminant anal ysis, discrimination and concept learning. Many practical applications relating to this field have been developed. New methods have appeared in recent years, due to developments concerning Neural Networks and M achine Learning. These ''hybrid'' approaches share one common factor i n that they combine symbolic and numerical aspects. The former are cha racterized by the representation of knowledge, the latter by the intro duction of frequencies and probabilistic criteria. In the present stud y, we shall present a certain number of hybrid methods, conceived (or improved) by members of the SYMENU research group. These methods issue mainly from Machine Learning and from research on Classification Tree s done in Statistics, and they may also be qualified as ''rule-based'' . They shall be compared with other more classical approaches. This co mparison will be based on a detailed description of each of the twelve methods envisaged, and on the results obtained concerning the ''Wavef orm Recognition Problem'' proposed by Breiman et al.,(4) which is diff icult for rule based approaches.