[Paper Review] Partial Gromov-Wasserstein Learning for Partial Graph Matching.

Weijie Liu, Chao Zhang+4 more|arXiv (Cornell University)|Dec 2, 2020

Advanced Graph Neural Networks50 references4 citations

TL;DR

This paper proposes a partial Gromov-Wasserstein learning framework for matching nodes between two graphs that overlap only partially, combining partial Gromov-Wasserstein and partial Wasserstein distances to jointly optimize the transport map and node embeddings. The method improves F1 scores by at least 20% on synthetic and real-world graphs, including heterogeneous graphs.

ABSTRACT

Graph matching finds the correspondence of nodes across two graphs and is a basic task in graph-based machine learning. Numerous existing methods match every node in one graph to one node in the other graph whereas two graphs usually overlap partially in many ealworld{} applications. In this paper, a partial Gromov-Wasserstein learning framework is proposed for partially matching two graphs, which fuses the partial Gromov-Wasserstein distance and the partial Wasserstein distance as the objective and updates the partial transport map and the node embedding in an alternating fashion. The proposed framework transports a fraction of the probability mass and matches node pairs with high relative similarities across the two graphs. Incorporating an embedding learning method, heterogeneous graphs can also be matched. Numerical experiments on both synthetic and ealworld{} graphs demonstrate that our framework can improve the F1 score by at least $20\%$ and often much more.

Motivation & Objective

• Address the limitation of existing graph matching methods that assume full node correspondence between graphs.
• Model real-world scenarios where graphs only partially overlap in structure and node content.
• Develop a unified framework that jointly optimizes node embeddings and transport maps for partial matching.
• Enable matching of heterogeneous graphs by incorporating an embedding learning component.
• Improve matching accuracy, particularly in terms of F1 score, over existing full-matching approaches.

Proposed method

• Formulate a joint objective combining partial Gromov-Wasserstein distance and partial Wasserstein distance to measure structural and feature-based similarity.
• Optimize the transport map and node embeddings in an alternating fashion to refine node correspondence.
• Allow partial mass transport, meaning only a fraction of the probability mass is moved, reflecting partial overlap.
• Use a differentiable framework to learn node embeddings that enhance similarity between matched node pairs.
• Support heterogeneous graph matching by integrating an embedding learning module into the optimization process.
• Leverage the structure of both graphs to identify high-similarity node pairs even when the graphs are not fully aligned.

Experimental results

Research questions

• RQ1 Can a unified learning framework effectively match nodes in two graphs with partial structural and feature overlap?
• RQ2 How does combining partial Gromov-Wasserstein and partial Wasserstein distances improve matching performance?
• RQ3 To what extent does the proposed method outperform full-matching baselines on partially overlapping graphs?
• RQ4 Can the framework generalize to heterogeneous graphs where node features differ across graphs?
• RQ5 What is the impact of joint optimization of transport maps and node embeddings on F1 score and matching accuracy?

Key findings

• The proposed framework improves the F1 score by at least 20% on both synthetic and real-world graph datasets.
• The method achieves significantly higher F1 scores than existing full-matching approaches, especially in scenarios with partial graph overlap.
• The framework successfully handles heterogeneous graphs by learning compatible node embeddings during optimization.
• Partial mass transport enables more realistic matching by focusing on high-similarity node pairs rather than forcing full correspondence.
• The alternating optimization of transport maps and embeddings leads to stable and improved convergence in node matching.
• Empirical results confirm the effectiveness of combining Gromov-Wasserstein and Wasserstein distances for partial graph matching.