Embedded Graph Learning

In this talk, we consider the simplest class of stratified spaces – linearly embedded graphs. We present a method to learns the abstract structure of an embedded graph and model 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.