Any Graph is a Mapper Graph

2024/08/20 by Alvarado, Enrique G, Belton, Robin, Lee, Kang-Ju +4 · 2 citations
#Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.11180

Abstract

The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset X and a graph G, does there exist a set of Mapper parameters such that the output Mapper graph of X is isomorphic to G? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph.

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• k-means considered harmful: On arbitrary topological changes in Mapper complexes
• A Stable and Theoretically Grounded Gromov-Wasserstein Distance for Reeb Graph Comparison using Persistence Images

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