Different Approaches to Clustering – Cassini Ovals

Abstract

Classical cluster analysis or clustering is the task of grouping of a set of objects in such a way that objects in the same group are more similar to each other than to those in other groups or clusters. There are many clustering algorithms for solving different tasks. In the research, an interesting method – Cassini oval – has been identified. The ovals of Cassini are defined to be the sets of points in the plane for which the product of the distances to two fixed points is constants. Cassini ovals are named after the astronomer Giovanni Domenico Cassini who studied them in 1680. Cassini believed that the Sun travelled around the Earth on one of these ovals, with the Earth at one focus of the oval. Other names include Cassinian ovals. A family of military applications of increasing importance is detection of a mobile target intruding into a protected area potentially well suited for this type of application of Cassini style method. The hypothesis is proposed that the Cassini ovals could be used for clustering purposes. The main aim of the research is to ascertain the suitability of Cassini ovals for clustering purposes.