A VALIDITY MEASURE FOR FUZZY CLUSTERING

Cluster analysis has been playing an important role in solving many problems in pattern recognition and image processing. This correspondence presents a fuzzy validity criterion based on a validity function which identifies overall compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids, and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function: the separation index, for which the condition of uniqueness has already been established. The performance evaluation of this validity function compares favorably to that of several others. Finally, we have applied this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing.