Optimal Transport for structured data with application on graphs

By Titouan Vayer, Nicolas Courty, Romain Tavenard, L. Chapel, Rémi Flamary. International Conference on Machine Learning, 2018

361 citations recorded by the source corpus.

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of the structured objects space. Unlike Wasserstein or Gromov-Wasserstein metrics that focus solely and respectively on features (by considering a metric in the feature space) or structure (by seeing structure as a metric space), our new distance exploits jointly both information, and is consequently called Fused Gromov-Wasserstein (FGW). After discussing its properties and computational aspects, we show results on a graph classification task, where our method outperforms both graph kernels and deep graph convolutional networks. Exploiting further on the metric properties of FGW, interesting geometric objects such as Frechet means or barycenters of graphs are illustrated and discussed in a clustering context.

View Paper: https://www.semanticscholar.org/paper/6f9de3cd77ac32ce00da3ba6b71e2360b5b2a81c

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Citations in the corpus

Projection-Free Optimization on Uniformly Convex Sets (2020, background): “…al., 2018), quadrature rules in RKHS (Bach et al., 2012; Lacoste-Julien et al., 2015; Futami et al., 2019), optimal transport (Courty et al., 2016; Vayer et al., 2018; Paty and Cuturi, 2019; Luise et al., 2019), and many others. x t +1 = (1 − γ t ) x t + γ t v t (cid:46) Convex update 5: end for…”
Graph Optimal Transport for Cross-Domain Alignment (2020, methodology): “Instead of using projected gradient descent or conjugated gradient descent as in Xu et al. (2019b;a); Vayer et al. (2018), we can approximate the transport plan T by adding back L uniﬁed in Algorithm 2, so that Line 9 in Algorithm 2 helps solve T for WD and GWD at the same time, effectively…”