Selection of Best Projection from 3D Star Coordinate Projection Space using Energy Minimization and Topology Preserving Mapping

This paper presents two algorithms for autonomously selecting the best projection among all possible configurations when projecting a high-dimensional (HD) data set on to a 3-dimensional (3D) space using 3D star coordinate projection (3D SCP). The proposed automated algorithms use two different objective functions that minimize the stress and preserve the pair wise distance among data points before and after the projection. The objective functions follow the principle of preserving topology similar to the multidimensional scaling (MDS). The concept of topology preserving mapping is found to be effective in autonomously selecting the best projection using the 3D SCP for visualization. Empirical analyses on artificial and real datasets are performed to show the utility of the proposed methods and their performances were also compared against linear and nonlinear projection-based visualization algorithms.