Validity of internal cluster indices

The evaluation of a clustering solution using cluster validity indices is necessary to identify the correct number of clusters, which is the fundamental consideration in clustering. Various techniques have been proposed in the literature to make advancements to the internal cluster validation. In this paper, various advancements in internal cluster validation like graph theory based indices, symmetry based indices, maximum intra-cluster distance based indices, separation and variance based indices, overlap and separation based indices, and density based indices have been reviewed. The impact of dimension, shape of cluster, size of cluster, density of cluster, noise, skewed distribution, overlap, and separation on the performance of the cluster validity indices have been analyzed to provide guidelines for selecting cluster validity indices for different clustering applications.