Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Vladyslav Oles (), Nathan Lemons and Alexander Panchenko
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Vladyslav Oles: Oak Ridge National Laboratory
Nathan Lemons: Oak Ridge National Laboratory
Alexander Panchenko: Oak Ridge National Laboratory

Journal of Combinatorial Optimization, 2024, vol. 48, issue 2, No 3, 36 pages

Abstract: Abstract Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library scikit-tda, and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

Keywords: Gromov–Hausdorff distance; Shape analysis; Network science; Anomaly detection (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01202-1

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