Year: 2018
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2804762181