ECKM: An improved K-means clustering based on computational geometry

Abstract

A modified version of traditional k-means clustering algorithm applying computational geometry for initialization of cluster centers has been presented in this paper. It is well known that the quality of k-means clustering depends on its random initialization of centers. This paper shows that when the initial cluster centers are selected from the list of circumference points of the empty circles sorted in non-increasing order of their corresponding radii, it can significantly improve the performance. The proposed algorithm is named as Empty Circles based k-means (ECKM) Clustering, which was successfully implemented with PYTHON. Extensive experimentation was carried out on various benchmark data sets that includes both artificial and real data sets having different shapes, sizes and features. In order to minimize the size of this paper, we presented the results for seven of such benchmark datasets, viz., iris, wine, hepta, flame compound, breast_cancer and DS577 although in reality we experimented for more than fifteen data sets in order to validate our ECKM. Results establish the superiority of the ECKM clustering over standard techniques.