General fuzzy min-max neural network for clustering and classification

Abstract

This paper describes a general fuzzy min-max (GFMM) neural network which is a generalization and extension of the fuzzy min-max clustering and classification algorithms developed by Simpson. The GFMM method combines the supervised and unsupervised learning within a single training algorithm. The fusion of clustering and classification resulted in an algorithm that can be used as pure clustering, pure classification, or hybrid clustering classification. This hybrid system exhibits an interesting property of finding decision boundaries between classes while clustering patterns that cannot be said to belong to any of existing classes. Similarly to the original algorithms, the hyperbox fuzzy sets are used as a representation of clusters and classes. Learning is usually completed in a few passes through the data and consists of placing and adjusting the hyperboxes in the pattern space which is referred to as an expansion-contraction process. The classification results can be crisp or fuzzy. New data can be included without the need for retraining. While retaining all the interesting features of the original algorithms, a number of modifications to their definition have been made in order to accommodate fuzzy input patterns in the form of lower and upper bounds, combine the supervised and unsupervised learning, and improve the effectiveness of operations. A detailed account of the GFMM neural network, its comparison with the Simpson's fuzzy min-max neural networks, a set of examples, and an application to the leakage detection and identification in water distribution systems are given.