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Abstract:
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Gromov-Wasserstein (GW) distance gives a way to compare probability distributions on different metric spaces by solving a quadratic programming problem inspired by optimal transport and Gromov-Hausdorff distance. Originally introduced by F. Mémoli, GW distance has found recent popularity in the machine learning community, where one frequently wants to compare distributions on a priori incomparable spaces such as networks. In this talk, I’ll describe a Riemannian structure on the space of networks, based on work of K. T. Sturm, for which GW distance is the geodesic distance. I’ll discuss applications to network analysis such as network partitioning—the unsupervised learning task of discovering communities in a network—where combining GW distance with spectral methods gives state-of-the-art results.
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