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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. • Goal: To develop internal Cluster Validity Indices for Arbitrary shape clusters. • Several CVIs are based on density intra- and inter-cluster measures. • Such density measures employ representative points to reduce the cost. • Our CVI results by some modifications of a recently introduced index (SSDD). • New CVI (SSDD-e) is effective also for clusters with gradually varying densities. [ABSTRACT FROM AUTHOR]

In this paper we address the problem of arbitrarily shaped clustering of points belonging to a linear space. Among the several approaches to clustering proposed in literature, the spectral clustering has become more and more popular for the case of arbitrarily shaped clusters. It depends on parameters whose choice can be critical. In order to reduce these criticalities, in this paper we propose a two-phase strategy that integrates the partitioning obtained by the spectral clustering with a merging technique which makes use only of the information already produced in the first phase by the spectral clustering. The main novelty of this approach is precisely the fact that no geometric tool is exploited in the merging phase. A numerical experimentation on artificial and real-world datasets has been performed to compare the proposed method with the spectral clustering and with two other widely used algorithms for non-convex problems, namely DBSCAN and Chameleon 2. • Arbitrarily shaped clustering is still a challenging problem. • Performance of Spectral Clustering (SC) depends on similarity matrix's parameters. • Proposed heuristic, based on two phases (SC + merging), reduces such a criticality. • Main novelty: merging does not exploit geometrical issues but only first step data. [ABSTRACT FROM AUTHOR]