Data analysis and the metric evolution of hypergraphs

TL;DR

This paper explores the use of Euclidean and Sobolev metrics to analyze the geometric evolution of hypergraphs generated by data point growth, aiming to improve differentiation of point distributions and dynamical systems.

Contribution

It introduces a novel approach combining Euclidean and Sobolev metrics to analyze hypergraph evolution for better data differentiation.

Findings

Hypergraph geometric signals can be effectively compared using Lebesgue and Sobolev norms.

The method provides reliable parameters for distinguishing point distributions.

The approach enhances understanding of hypergraph dynamics in data analysis.

Abstract

In this paper we aim to use different metrics in the Euclidean space and Sobolev type metrics in function spaces in order to produce reliable parameters for the differentiation of point distributions and dynamical systems. The main tool is the analysis of the geometrical evolution of the hypergraphs generated by the growth of the radial parameters for a choice of an appropriate metric in the space containing the data points. Once this geometric dynamics is obtained we use Lebesque and Sobolev type norms in order to compare the basic geometric signals obtained.