Validity index for clustering with penalizing method

One of the most difficult problems facing the user of clustering analysis techniques in practice is the objective assessment of the stability and validity of the clusters found by the numerical technique used. The problem of determining the “true” number of clusters has been called the fundamental problem of cluster validity. In this paper, a validity index for clustering with penalizing method is proposed, maximization of which ensures the formation of a small number of compact clusters with large separation between at least two clusters. Experimental results are provided to demonstrate the superiority of this index as compared to five well-known validity indexes by using the k-means and fuzzy c-means algorithms.