Learning Simplicial Complexes from Persistence Diagrams
Abstract
Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that one can reconstruct a simplicial complex embedded in R^3 using persistence diagrams generated from all possible height filtrations (an uncountably infinite number of directions). In this paper, we present an algorithm for reconstructing plane graphs K=(V,E) in R^2 , i.e., a planar graph with vertices in general position and a straight-line embedding, from a quadratic number height filtrations and their respective persistence diagrams.
Cite
@article{arxiv.1805.10716,
title = {Learning Simplicial Complexes from Persistence Diagrams},
author = {Robin Lynne Belton and Brittany Terese Fasy and Rostik Mertz and Samuel Micka and David L. Millman and Daniel Salinas and Anna Schenfisch and Jordan Schupbach and Lucia Williams},
journal= {arXiv preprint arXiv:1805.10716},
year = {2018}
}
Comments
Updated our document for clarity in response to comments by reviewers at CCCG. This paper will appear at CCCG 2018