Graph Diffusion Wasserstein Distances

Optimal Transport (OT) for structured data has received much attention in the machine learning community, especially for addressing graph classification or graph transfer learning tasks. In this paper, we present the Diffusion Wasserstein (DW $$\mathtt {DW}$$ ) distance, as a generalization of the s...

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Bibliographic Details
Published inMachine Learning and Knowledge Discovery in Databases Vol. 12458; pp. 577 - 592
Main Authors Barbe, Amélie, Sebban, Marc, Gonçalves, Paulo, Borgnat, Pierre, Gribonval, Rémi
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2021
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Graph Laplacian
Heat diffusion
Optimal Transport
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ISBN3030676609
9783030676605
ISSN0302-9743
1611-3349
DOI10.1007/978-3-030-67661-2_34

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Summary:Optimal Transport (OT) for structured data has received much attention in the machine learning community, especially for addressing graph classification or graph transfer learning tasks. In this paper, we present the Diffusion Wasserstein (DW $$\mathtt {DW}$$ ) distance, as a generalization of the standard Wasserstein distance to undirected and connected graphs where nodes are described by feature vectors. DW $$\mathtt {DW}$$ is based on the Laplacian exponential kernel and benefits from the heat diffusion to catch both structural and feature information from the graphs. We further derive lower/upper bounds on DW $$\mathtt {DW}$$ and show that it can be directly plugged into the Fused Gromov Wasserstein (FGW $$\mathtt {FGW}$$ ) distance that has been recently proposed, leading - for free - to a DifFused Gromov Wasserstein distance (DFGW $$\mathtt {DFGW}$$ ) that allows a significant performance boost when solving graph domain adaptation tasks.
Bibliography:Electronic supplementary materialThe online version of this chapter (https://doi.org/10.1007/978-3-030-67661-2_34) contains supplementary material, which is available to authorized users.
Original Abstract: Optimal Transport (OT) for structured data has received much attention in the machine learning community, especially for addressing graph classification or graph transfer learning tasks. In this paper, we present the Diffusion Wasserstein (DW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {DW}$$\end{document}) distance, as a generalization of the standard Wasserstein distance to undirected and connected graphs where nodes are described by feature vectors. DW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {DW}$$\end{document} is based on the Laplacian exponential kernel and benefits from the heat diffusion to catch both structural and feature information from the graphs. We further derive lower/upper bounds on DW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {DW}$$\end{document} and show that it can be directly plugged into the Fused Gromov Wasserstein (FGW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {FGW}$$\end{document}) distance that has been recently proposed, leading - for free - to a DifFused Gromov Wasserstein distance (DFGW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {DFGW}$$\end{document}) that allows a significant performance boost when solving graph domain adaptation tasks.
ISBN:3030676609
9783030676605
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-67661-2_34