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- W4288103677 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 polynomial algorithm for estimating the so-called modified Gromov-Hausdorff (mGH) distance, whose topological equivalence with the standard Gromov-Hausdorff (GH) distance was established in cite{memoli12} (M'emoli, F, textit{Discrete & Computational Geometry, 48}(2) 416-440, 2012). We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library verb|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." @default.
- W4288103677 created "2022-07-28" @default.
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- W4288103677 date "2019-09-21" @default.
- W4288103677 modified "2023-10-16" @default.
- W4288103677 title "Efficient estimation of a Gromov--Hausdorff distance between unweighted graphs" @default.
- W4288103677 doi "https://doi.org/10.48550/arxiv.1909.09772" @default.
- W4288103677 hasPublicationYear "2019" @default.
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