Deep Graph Matching Consensus (2001.09621v1)

Abstract: This work presents a two-stage neural architecture for learning and refining structural correspondences between graphs. First, we use localized node embeddings computed by a graph neural network to obtain an initial ranking of soft correspondences between nodes. Secondly, we employ synchronous message passing networks to iteratively re-rank the soft correspondences to reach a matching consensus in local neighborhoods between graphs. We show, theoretically and empirically, that our message passing scheme computes a well-founded measure of consensus for corresponding neighborhoods, which is then used to guide the iterative re-ranking process. Our purely local and sparsity-aware architecture scales well to large, real-world inputs while still being able to recover global correspondences consistently. We demonstrate the practical effectiveness of our method on real-world tasks from the fields of computer vision and entity alignment between knowledge graphs, on which we improve upon the current state-of-the-art. Our source code is available under https://github.com/rusty1s/ deep-graph-matching-consensus.

• The paper introduces a two-stage neural architecture that computes initial soft correspondences through localized node embeddings.
• It refines these correspondences using synchronous message passing to achieve neighborhood consensus for improved graph matching.
• Empirical results show superior performance on tasks such as computer vision and knowledge graph alignment compared to existing methods.

An Analytical Overview of Deep Graph Matching Consensus

The paper "Deep Graph Matching Consensus" introduces a two-stage neural architecture designed for learning and refining structural correspondences between graph nodes. Graph matching, the core problem addressed by the paper, involves establishing meaningful structural correspondences of nodes between graphs, considering both node and pairwise edge similarities. This problem is central to applications such as computer vision, bioinformatics, social network analysis, and cheminformatics, where graphs serve as natural representations of relational data.

Methodological Approach

The proposed architecture includes two distinct stages for processing graph data:

1. Initial Matching through Localized Node Embeddings:
   • The first stage employs a Graph Neural Network (GNN) to compute localized node embeddings. These embeddings generate an initial ranking of what the paper terms "soft correspondences" between nodes of different graphs. This stage relies on the node's feature similarity for the initial matching.
2. Refinement through Synchronous Message Passing:
   • The second stage iteratively refines the soft correspondences obtained in the first stage. This refinement aims to reach a "matching consensus" by employing synchronous message-passing networks to make the correspondences consistent across the graph's local neighborhoods.

The synchronous message-passing mechanism effectively computes a consensus measure that guides the re-ranking process. By sampling and distributing functional mappings across the neighborhoods, it ensures that adjacent nodes in the source graph map consistently within the target graph.

Empirical and Theoretical Validation

This paper shows both theoretical robustness and practical efficacy of the proposed architecture:

• Theoretical Foundations: The paper rigorously proves that the message-passing scheme they propose computes a robust measure of consensus across corresponding graph neighborhoods. Two theorems in the paper detail how permutation equivariant GNNs assure neighborhood consensus, helping to ensure effective matching refinement.
• Empirical Results: The architecture demonstrated practical effectiveness on tasks in computer vision and knowledge graph entity alignment, consistently outperforming current state-of-the-art methods.

Scalable and Sparse Awareness

A notable advantage of the proposed method is its scalability and ability to handle sparsity effectively. This is vital because large, real-world graphs often demand algorithms that can scale efficiently. The architecture focuses on purely local and sparsity-aware processes, which scale well to large inputs while maintaining the ability to recover global correspondences. By filtering out low-probability correspondences and focusing on top candidates, the computational overhead is minimized, especially in large input domains like knowledge graphs.

Implications and Future Directions

The implications of this research span both theoretical advancements in graph neural networks and practical applications for graph-based data analysis tasks. The approach exemplifies how deep learning can be utilized not just for generic node or graph embedding tasks, but also for specific problems like graph matching where structure and correspondence refinement are critical. Future work might explore further advancements in architecture, including potentially integrating higher-order features or more complex similarities into the matching algorithm. Given the continued evolution of large-scale networks and graph-structured data, this work paves the way for the development of more efficient and accurate graph processing techniques.

In summary, "Deep Graph Matching Consensus" successfully integrates theoretical innovation with practical application, offering a robust solution to the complex problem of graph matching with enhancements in local consensus modeling and scalable processing. Such contributions make it a significant step forward in the application of neural networks to graph-structured data.