Stratified Space Learning: Reconstructing Embedded Graphs

TL;DR

This paper introduces a method for reconstructing embedded graph structures from noisy data using topological data analysis combined with numerical modeling, aiding in data understanding and simulation.

Contribution

It presents a novel approach to recover and model the structure of embedded graphs from noisy high-dimensional data samples.

Findings

Successfully reconstructs graph structures from noisy data

Combines topological analysis with numerical modeling techniques

Enhances data structure discovery in high-dimensional spaces

Abstract

Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional spaces. The modelling of these underlying structures is also beneficial for the creation of simulated data that better represents real data. In particular, for systems testing in cases where the use of real data streams might prove impractical or otherwise undesirable. We seek to discover and model the structure by combining methods from topological data analysis with numerical modelling. As a first step in combining these two areas, we examine the recovery of the abstract graph $G$ structure, and model a linear embedding $|G|$ given only a noisy point cloud sample $X$ of $|G|$.