A Cluster Validity Index for Fuzzy Clustering Based on Non-distance

Aiming at the weak points of fuzzy cluster validity indexes that measure compactness within cluster and separation between clusters based on distance, we propose a new non-distance cluster index. Firstly, we analyze that validity index based on distance can't recognize overlapping clusters and is sensitive to noisy data. Secondly, we measure compactness within cluster and separation between clusters by using relation of membership, and construct equation of compactness and separation. Finally, we synthesize compactness and separation to form non-distance equation of validity index. Experiments on artificial data show that new index not only recognizes overlapping clusters but also is insensitive to noisy data, and has more efficiency.