Automatic Training of Min-Max Classifiers

Although the most important feature of a classifier is its generalization capability, the effectiveness of a training procedure is strictly related to its automation degree. A low automation degree can be a serious drawback for a classification system, since it can prevent an unskilled user from successfully generating an acceptable model. From this point of view, a learning procedure should not depend on any critical parameter. Among fuzzy classifiers, Min-Max networks have the advantage to be trained in a constructive way, with a simple learning procedure. The use of the hyperbox as a frame on which different membership functions can be modeled, makes the Min-Max network a flexible tool. The present chapter focuses on Fuzzy Min-Max networks and on improved versions recently developed in order to overcome some inconveniences. By relying on a basic principle of Learning Theory, a simple technique to improve generalization capability will be described. The application of this technique to the Min-Max fuzzy classifier yields the Optimized Min-Max training algorithm (OMM), which is able to choose automatically a critical parameter that affects the original Simpson's learning procedure. However, OMM still exhibits the same inconveniences that characterize Min-Max learning; in particular there is an excessive dependence on the presentation order of the training set and the coverage resolution is constrained to be the same in the overall input space. The Adaptive Resolution Classifier (ARC) is a batch training algorithm for Min-Max Fuzzy networks able to overcome these drawbacks. ARC is characterized by a high automation degree and allows obtaining networks with a remarkable generalization capability. In order to further improve the reconstruction capability of the decision region, it is necessary to consider a new type of fuzzy neural network. By adopting the Generalized Min-Max model (GMM) it is possible to arrange the hyperbox orientation along any direction of the data space. A suitable training algorithm (GPARC) can be used for the automatic determination of the optimal GMM model. The performances of ARC, PARC and GPARC training algorithms will be discussed through a set of bidimensional toy problems and real data benchmarks.