On a linear fused Gromov-Wasserstein distance for graph structured data

Abstract:We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named linearFGW, defined as the Euclidean distance between their embeddings. The advantages of the proposed distance are twofold: 1) it can take into account node feature and structure of graphs for measuring the similarity between graphs in a kernel-based framework, 2) it can be much faster for computing kernel matrix than pairwise OT-based distances, particularly fused Gromov-Wasserstein, making it possible to deal with large-scale data sets. After discussing theoretical properties of linearFGW, we demonstrate experimental results on classification and clustering tasks, showing the effectiveness of the proposed linearFGW.

Machine Learning (cs.LG)

arXiv:2203.04711 [cs.LG]

(or arXiv:2203.04711v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2203.04711 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1016/j.patcog.2023.109351 Focus to learn more DOI(s) linking to related resources

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