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

• URL: http://arxiv.org/abs/2203.04711v1
• Date: Wed, 9 Mar 2022 13:43:18 GMT
• Title: On a linear fused Gromov-Wasserstein distance for graph structured data
• Authors: Dai Hai Nguyen, Koji Tsuda
• Abstract summary: 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.
• Score: 2.360534864805446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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