On the gravitation-based classification: A novel algorithm using equilibrium points for enhanced learning and dimensionality reduction

The concept and effects of gravitation have been effectively utilized to design various data classification algorithms. Generally, there are two primary approaches to gravitation-based classification: one that relies on gravitational force and another that is based on gravitational potential energy. In this paper, we examine these two approaches and introduce a novel classification algorithm grounded in gravitational potential energy. The core idea of our approach is to identify an equilibrium point for a line mass (serving as the classifier line) situated between two groups of fixed point masses (representing two data classes). The equilibrium point of the classifier line is determined by minimizing the total gravitational potential energy resulting from the two groups of point masses. Notably, our method demonstrates the following: (i) it acts as a dimensionality reduction technique that seeks a new feature space with lower dimensionality for improved class discrimination by maximizing the sum of the logarithms of the projections, (ii) it leads to an information-theoretic learning strategy that minimizes the overall uncertainty of the classifier, and (iii) it offers a convex formulation that guarantees convergence to a global optimum solution. We also present experimental results that indicate the superior performance of the proposed method compared to existing techniques.