Cluster validity index based on n-sphere

In this paper, we propose a new cluster validity index (CVI) based on geometrical shape. Classic CVIs are based on a combination of separation and compactness measures and may include a measure of overlap between clusters. The proposed CVI combines measures of compactness and over-lap using n-sphere shape. We conducted experiments on several real data sets from the UCI repository and compared the performances of the proposed CVI with widely used CVIs. Results demonstrate that the proposed CVI performs better than the others even when used with complicated data sets.