A validity measure for fuzzy clustering and its use in selecting optimal number of clusters

Cluster analysis has been playing an important role in solving many problems in pattern recognition and image processing. If fuzzy cluster analysis is to make a significant contribution to engineering applications, much more attention must be paid to fundamental decision on the number of clusters in data. It is related to cluster validity problem of how well it has identified the structure that is present in the data. In this paper, we define I_G as a fuzzy clustering validity function which measures the overall average compactness and separation of fuzzy c-partition and propose a new approach to selecting optimal number of clusters using the measurement value of I_G. This approach uses relative values and normalized value of I_G and it does not require human interpretation. It is compared with conventional validity functions, partition coefficient and CSC index, on the several data sets