Learning Simplicial Complexes from Persistence Diagrams

05/27/2018

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by   Robin Lynne Belton, et al.

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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.