A performance measure for the fuzzy cluster validity

The primary concern with the use of any clustering is how well it has identified the structure that is present in the data. This is the “cluster validity problem”. In this paper, we define G as a measure of the quality of clustering which is based on the mini-max filter concept and fuzzy theory. It measures the overall average compactness and separation of a fuzzy c-partition and explore the properties of G, and we define I_G as a more suitable measure to compare the clustering result of one fuzzy c₁-partition with another c₂-partition of a data set. We show the measure I_G can be used to select an optimal number of clusters