A new approach for measuring the validity of the fuzzy c-means algorithm

In this paper an index to validate the fuzzy c-means algorithm is developed. The proposed index adopts a compactness measure to describe the variation of clusters, and introduces the fuzzy separation concept to determine the isolation of clusters. The basic design element of fuzzy separation is the fuzzy deviation between two cluster centers, which is calculated by taking into account the locations of the rest of the centers. Limiting analysis indicates the sensitivity of the index with respect to the design parameters, while the application to two data sets illustrates the effectiveness of the index in detecting the correct fuzzy c-partitions.