An internal validity index for arbitrarily shaped clusters

We examine in this paper some internal CVIs (cluster validity indices) especially designed for the validation of arbitrarily shaped clusters, for example nonconvex clusters or clusters that nearly touch each other or are embedded into other clusters. They are based on the identification of multi-representative points for each cluster and on density considerations. In general, they target clusters characterized by cores of high density surrounded by regions of low density. Such a characterization is exploited to evaluate the separation among clusters, but can be a serious limitation for example when the clusters have high density regions in peripheral positions close to individual borders or have internal regions of non uniform density. Among the CVIs taken into consideration, we especially single out the SSDD index introduced in Liang et al. (2020) and propose some modifications for extending its applicability field. A numerical experimentation on both artificial and real-world datasets has been performed, confirming the effectiveness of the proposed modified index with respect to SSDD index and to other multi-representative CVIs described in literature.