Using topological autoencoders as a filtering function for global and local topology

TL;DR

This paper explores the use of topological autoencoders as a universal filtering function for the Mapper algorithm, aiming to improve the representation of high-dimensional manifolds across various domains.

Contribution

It proposes topological autoencoders as a general filtering function for Mapper, demonstrating initial results that support its effectiveness for high-dimensional data.

Findings

Potential for easier filtering function selection in Mapper

Improved representation of high-dimensional manifolds

Initial positive results on high-dimensional datasets

Abstract

Choosing a suitable filtering function for the Mapper algorithm can be difficult due to its arbitrariness and domain-specific requirements. Finding a general filtering function that can be applied across domains is therefore of interest, since it would improve the representation of manifolds in higher dimensions. In this extended abstract, we propose that topological autoencoders is a suitable candidate for this and report initial results strengthening this hypothesis for one set of high-dimensional manifolds. The results indicate a potential for an easier choice of filtering function when using the Mapper algorithm, allowing for a more general and descriptive representation of high-dimensional data.