A Novel 2D Clustering Algorithm Based on Recursive Topological Data Structure

Abstract

In the field of data science and data mining, the problem associated with clustering features and determining its optimum number is still under research consideration. This paper presents a new 2D clustering algorithm based on a mathematical topological theory that uses a pseudometric space and takes into account the local and global topological properties of the data to be clustered. Taking into account cluster symmetry property, from a metric and mathematical-topological point of view, the analysis was carried out only in the positive region, reducing the number of calculations in the clustering process. The new clustering theory is inspired by the thermodynamics principle of energy. Thus, both topologies are recursively taken into account. The proposed model is based on the interaction of particles defined through measuring homogeneous-energy criterion. Based on the energy concept, both general and local topologies are taken into account for clustering. The effect of the integration of a new element into the cluster on homogeneous-energy criterion is analyzed. If the new element does not alter the homogeneous-energy of a group, then it is added; otherwise, a new cluster is created. The mathematical-topological theory and the results of its application on public benchmark datasets are presented.