Reconstructing linearly embedded graphs: A first step to stratified space learning
Yossi Bokor Bleile, Katharine Turner, Christopher Williams · Foundations of Data Science · 2021
In this paper, we consider the simplest class of stratified spaces – linearly embedded graphs. We present an algorithm that learns the abstract structure of an embedded graph and models the specific embedding from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding. The algorithm is implemented in the Julia package Skyler, which we used for the numerical simulations in this paper. Erratum: Nanda et al. should be Stolz et al. in both the PDF (page 2, line 6) and HTML versions of this paper. We apologize for any inconvenience this may cause.