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This paper presents a novel geometrical approach to investigate the convexityof a density-based cluster. Our approach is grid-based and we are about tocalibrate the value space of the cluster. However, the cluster objects arecoming from an infinite distribution, their number is finite, and thus, theregarding shape will not be sharp. Therefore, we establish the precision of thegrid properly in a way that, the reliable approximate boundaries of the clusterare founded. After that, regarding the simple notion of convex sets andmidpoint convexity, we investigate whether or not the density-based cluster isconvex. Moreover, our experiments on synthetic datasets demonstrate thedesirable performance of our method.

A Grid-based Approach for Convexity Analysis of a Density-based Cluster