Nuclear Potential Clustering As a New Tool to Detect Patterns in High Dimensional Datasets

Abstract

We present a new approach for the clustering of high dimensional data without prior assumptions about the structure of the underlying distribution. The proposed algorithm is based on a concept adapted from nuclear physics. To partition the data, we model the dynamic behaviour of nucleons interacting in an N-dimensional space. An adaptive nuclear potential, comprised of a short-range attractive (strong interaction) and a long-range repulsive term (Coulomb force) is assigned to each data point. By modelling the dynamics, nucleons that are densely distributed in space fuse to build nuclei (clusters) whereas single point clusters repel each other. The formation of clusters is completed when the system reaches the state of minimal potential energy. The data are then grouped according to the particles' final effective potential energy level. The performance of the algorithm is tested with several synthetic datasets showing that the proposed method can robustly identify clusters even when complex configurations are present. Furthermore, quantitative MRI data from 43 multiple sclerosis patients were analyzed, showing a reasonable splitting into subgroups according to the individual patients' disease grade. The good performance of the algorithm on such highly correlated non-spherical datasets, which are typical for MRI derived image features, shows that Nuclear Potential Clustering is a valuable tool for automated data analysis, not only in the MRI domain.