A New Fuzzy Clustering Validity Index With a Median Factor for Centroid-Based Clustering

Determining the number of clusters, which is usually approved by domain experts or evaluated by clustering validity indexes, is an important issue in clustering analysis. This study discusses the effectiveness of clustering validity indexes for centroid-based partitional clustering algorithms. Most general-purpose clustering validity indexes take the minimum/maximum distance between a pair of data objects, a pair of cluster centroids, or an object and a centroid as an important evaluation factor; however, they may present unstable results, especially when two centroids are allocated closely. To alleviate this problem, a new clustering validity index, which is termed the Wu-and-Li index (WLI), is proposed in this paper. Our proposed WLI partially allows, to some extent, the existence of closely allocated centroids in the clustering results by considering not only the minimum but the median distances between a pair of centroids as well; therefore possessing better stability. The performances of WLI and some existing clustering validity indexes are evaluated and compared by running the fuzzy c-means algorithm for clustering various types of datasets, including artificial datasets, UCI datasets, and images. Experimental results have shown that WLI has the more accurate and satisfactory performance than other indexes.