A new cluster validity criterion for the cross iterative fuzzy clustering algorithm

Many criteria have been proposed for clustering validity analysis in the literature. With a new definition of fuzzy compactness and fuzzy separation, a new cluster validity criterion is proposed for the cross iterative fuzzy clustering algorithm, which considers two kinds of outputs of fuzzy clustering: the geometrical properties of data and the fuzzy memberships, and has two terms: the ratio of fuzzy compactness to average fuzzy separation and the ratio of fuzzy union to fuzzy intersection of clusters. A weighting parameter is introduced to reflect the role of these two terms in validity analysis. The experimental analysis testifies that the minimum of the proposed criterion is a fine indicator for a compact and well-separated partition.