Fuzzy Cluster Validity Index Based on Object Proximities Defined over Fuzzy Partition Matrices

Cluster validity index algorithms, which find the number of clusters in a given object set, play an important role in clustering. There have been many proposals of cluster validity index, especially for fuzzy clustering, and many of them are dependent on clustering algorithms that can use the different interpretations of similarities between objects, usually in the geometric interpretation of objects. We present a new fuzzy cluster validity index that is independent of clustering algorithms. The index uses the concept of distinguishableness of clusters, which is measured based on the object proximities defined over a given fuzzy partition matrix. We show the effectiveness of the proposed index by comparing it to other indices, with the fuzzy partition matrices obtained using the Fuzzy C-Means algorithm over various synthetic object sets.