A cluster validity index for fuzzy clustering

In this paper, a cluster validity index proposed by Kim et al. [15] is analyzed, and a problem is discussed that the validity index faces in situations when there are well-separated clusters that themselves include subclusters. Based on this analysis, a new validity index is proposed. The new validity index employs a compactness measure and a separation measure. The compactness measure combines the fuzziness in the membership matrix (U) with the geometrical compactness of the representation of the data set (X) via the prototypes (V). The separation measure is defined as the average value of the degrees of overlap of all possible pairs of fuzzy clusters in the system. The proposed index is tested and validated using several data sets. The results of the comparison show the superior effectiveness and reliability of the proposed index in comparison to other indices.