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 eachother or are embedded into other clusters. They are based on the identificationof multi-representative points for each cluster and on densityconsiderations. In general, they target clusters characterized by coresof high density surrounded by regions of low density. Such a characterizationis exploited to evaluate the separation among clusters, but canbe a serious limitation for example when the clusters have high densityregions in peripheral positions close to individual borders or haveinternal regions of non uniform density. Among the CVIs taken intoconsideration, we especially single out the SSDD index introduced in(Liang et al., 2020) and propose some modifications for extending itsapplicability field. A numerical experimentation on both artificial andreal-world datasets has been performed, confirming the effectiveness ofthe proposed modified index with respect to SSDD index and to othermulti-representative CVIs described in literature.