Classification validity index

Abstract

A validity index of the partition of the data space is a fundamental tool for parameter selection in pattern recognition techniques. Particularly when the number of classes is unknown and whenever overlapping may occur, self learning, or clustering, algorithms take advantage of a self evaluation of the goodness of the result. In the LAMDA classification and learning approach the family of adequacy functions and the aggregation operators can be adjusted according to the quality of the result. Validity index proposed here leads towards the optimal class number in a fuzzy partition for a given data set. The index developed here is a fuzzy extension of a known compactness and separation validity coefficient especially when there is high overlapping among classes and the former index cannot be applied, it allows evaluating the optimal number of classes and improves the partition quality. Several applications to industrial plants have been implemented with this validity index.