Determining Distribution of a Seven-Dimensional Point Cluster with a Novel Hypersphere Method

This paper introduces a novel method for analysing high-dimensional data points called the Most-Distant Uncovered Point (MDUP) hypersphere method. The MDUP method is a binary classification technique that defines equidistant N-dimensional points as unions of hyperspheres. The method iteratively creates hyperspheres at the most distant point within the region of interest until the entire region is covered. Tested on a 7-dimensional space representing feasible and infeasible model parameters for a cardiovascular system model, the MDUP hypersphere method tends to generate a few large spheres away from the boundary and numerous small spheres around the boundary to fill the space. The MDUP method can scale to any dimension, needing only centre points and radii, providing easily interpretable results. It can also identify large continuous regions and capture the general structure with few hyperspheres. Additionally, the method has potential to generate optimising algorithm starting conditions within predefined feasible regions, potentially enhancing model identifiability and optimisation results. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)