Nudged Elastic Band in Topological Data Analysis

TL;DR

This paper adapts the nudged elastic band method from chemistry to topological data analysis, producing cell complexes that model dense data regions and revealing new topological structures in complex datasets.

Contribution

It introduces a novel application of the nudged elastic band method to topological data analysis, inspired by Morse theory, for modeling dense data regions.

Findings

Successfully applied to social network and image processing datasets

Revealed new topological structures in optical flow patches

Produced a sequence of cell complexes representing data density

Abstract

We use the nudged elastic band method from computational chemistry to analyze high-dimensional data. Our approach is inspired by Morse theory, and as output we produce an increasing sequence of small cell complexes modeling the dense regions of the data. We test the method on data sets arising in social networks and in image processing. Furthermore, we apply the method to identify new topological structure in a data set of optical flow patches.