[Paper Review] Neural Subgraph Matching

Zhitao Ying, Andrew Wang+5 more|arXiv (Cornell University)|Jul 6, 2020

Graph Theory and Algorithms42 references41 citations

TL;DR

NeuroMatch uses graph neural networks and order-embedding geometry to efficiently determine if a query graph is a subgraph of a large target graph, outperforming existing methods in speed and accuracy.

ABSTRACT

Subgraph matching is the problem of determining the presence and location(s) of a given query graph in a large target graph. Despite being an NP-complete problem, the subgraph matching problem is crucial in domains ranging from network science and database systems to biochemistry and cognitive science. However, existing techniques based on combinatorial matching and integer programming cannot handle matching problems with both large target and query graphs. Here we propose NeuroMatch, an accurate, efficient, and robust neural approach to subgraph matching. NeuroMatch decomposes query and target graphs into small subgraphs and embeds them using graph neural networks. Trained to capture geometric constraints corresponding to subgraph relations, NeuroMatch then efficiently performs subgraph matching directly in the embedding space. Experiments demonstrate NeuroMatch is 100x faster than existing combinatorial approaches and 18% more accurate than existing approximate subgraph matching methods.

Motivation & Objective

• Address the NP-complete subgraph isomorphism problem in large graphs.
• Develop a neural approach that scales to large target and query graphs.
• Leverage k-hop neighborhood embeddings and order embeddings to preserve subgraph relations.
• Enable offline target graph embedding and fast, embedding-space query matching.
• Demonstrate superior speed and accuracy over traditional and neural baselines.

Proposed method

• Decompose both target G_T and query G_Q into small overlapping k-hop neighborhoods around each node.
• Embed each k-hop neighborhood with a graph neural network to obtain node embeddings z_u.
• Use order embeddings to enforce a partial order reflecting subgraph relationships (z_q to be coordinate-wise <= z_u when G_q ⊆ G_u).
• Train with max-margin loss E(z_q,z_u)=||max{0,z_q−z_u}||_2^2 over positive/negative pairs.
• Define subgraph prediction f(z_q,z_u) = 1 if E(z_q,z_u) < t, else 0, enabling fast query-stage scoring.
• During query, compute embeddings for G_Q nodes and compare with precomputed G_T embeddings to predict subgraph matches, using a voting-based refinement based on neighborhood consistency.

Experimental results

Research questions

• RQ1 Can a neural model learn to represent subgraph containment via a geometric, partial-order embedding space?
• RQ2 How can we efficiently determine subgraph relationships using embeddings rather than combinatorial search?
• RQ3 Does offline embedding of target graphs enable fast, scalable querying for new subgraph queries?
• RQ4 Do order-embedding based models outperform traditional and other neural baselines in accuracy and speed for subgraph matching?
• RQ5 Is the approach robust to different sampling strategies and dataset domains?

Key findings

• NeuroMatch achieves up to 100x speedup over exact combinatorial methods and 18% AUROC improvement over neural baselines on subgraph matching tasks.
• Using order embeddings yields a median AUROC around 95.5 across tested datasets, outperforming neural baselines by ~20% on Problem 2.
• The curriculum training strategy improves performance by about 6% on average and enhances convergence.
• NeuroMatch scales linearly with query size and target size in practice, contrasting with exponential time of exact methods.
• Embeddings preserve subgraph relations via a transitive, antisymmetric partial order, enabling efficient query-time reasoning.