An Efficient Algorithm for Clustering of Convex and Non-Convex Data

In this paper, using the concepts of field theory and potential functions, an optimal algorithm for clustering the convex and non-convex data is proposed. For this purpose, equipotential surfaces, created by the interaction of the potential functions, are applied. Equipotential surfaces are the geometric location of the points in the space on which the potential is constant. It means all points in each surface affected the same from the field. Regarding this concept and characteristics of equipotential surfaces, the outcome of this method will be an optimal solution for the clustering problem. But with regard to the existence of several parameters requiring to be set in the algorithm, finding the global optimal solution needs a very high computational complexity and therefore is not practical. Thus by applying some considerations and approximations, the resulting outcome will be a suboptimal solution, while appropriate setting of the parameters causes the result to be closer to the global optimal solution. Simulation results for a number of standard data-sets, illustrates the superb performance of this method, especially for non-convexly scattered data.

Keywords:

Clustering , Convex , Non-Convex , Norm Space , Potential Functions , Unsupervised and Sub-Optimal