Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Subgraph Matching via Partial Optimal Transport

Wen-Xin Pan, Isabel Haasler, Pascal Frossard

TL;DR

This paper addresses subgraph matching by formulating it as a partial fused Gromov-Wasserstein problem, enabling soft, robust matching between a query graph and subgraphs of a large source graph. It introduces Subgraph Optimal Transport (SOT) and Sliding Subgraph Optimal Transport (SSOT), where SOT solves a partial FGW between the source and query graphs (augmented with a dummy node) and SSOT accelerates this process by sliding small k-hop subgraphs and pruning candidates with a cheap bound. The approach is shown to outperform state-of-the-art methods on both synthetic Erdős–Rényi graphs and real-world networks, particularly under feature noise and for large graphs, while maintaining competitive or superior query times. Overall, the work provides a principled, scalable, and noise-robust distance-based framework for subgraph matching with practical implications for anomaly detection and knowledge discovery.

Abstract

In this work, we propose a novel approach for subgraph matching, the problem of finding a given query graph in a large source graph, based on the fused Gromov-Wasserstein distance. We formulate the subgraph matching problem as a partial fused Gromov-Wasserstein problem, which allows us to build on existing theory and computational methods in order to solve this challenging problem. We extend our method by employing a subgraph sliding approach, which makes it efficient even for large graphs. In numerical experiments, we showcase that our new algorithms have the ability to outperform state-of-the-art methods for subgraph matching on synthetic as well as realworld datasets. In particular, our methods exhibit robustness with respect to noise in the datasets and achieve very fast query times.

Subgraph Matching via Partial Optimal Transport

TL;DR

This paper addresses subgraph matching by formulating it as a partial fused Gromov-Wasserstein problem, enabling soft, robust matching between a query graph and subgraphs of a large source graph. It introduces Subgraph Optimal Transport (SOT) and Sliding Subgraph Optimal Transport (SSOT), where SOT solves a partial FGW between the source and query graphs (augmented with a dummy node) and SSOT accelerates this process by sliding small k-hop subgraphs and pruning candidates with a cheap bound. The approach is shown to outperform state-of-the-art methods on both synthetic Erdős–Rényi graphs and real-world networks, particularly under feature noise and for large graphs, while maintaining competitive or superior query times. Overall, the work provides a principled, scalable, and noise-robust distance-based framework for subgraph matching with practical implications for anomaly detection and knowledge discovery.

Abstract

In this work, we propose a novel approach for subgraph matching, the problem of finding a given query graph in a large source graph, based on the fused Gromov-Wasserstein distance. We formulate the subgraph matching problem as a partial fused Gromov-Wasserstein problem, which allows us to build on existing theory and computational methods in order to solve this challenging problem. We extend our method by employing a subgraph sliding approach, which makes it efficient even for large graphs. In numerical experiments, we showcase that our new algorithms have the ability to outperform state-of-the-art methods for subgraph matching on synthetic as well as realworld datasets. In particular, our methods exhibit robustness with respect to noise in the datasets and achieve very fast query times.
Paper Structure (15 sections, 2 theorems, 23 equations, 5 figures, 3 tables, 2 algorithms)

This paper contains 15 sections, 2 theorems, 23 equations, 5 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Optimal transport and partial optimal transport
  4. Fused Gromov-Wasserstein distance for graphs
  5. SOT: Subgraph optimal transport
  6. SSOT: Sliding Subgraph Optimal Transport
  7. Experiments
  8. Experiments on Erdős–Rényi graphs
  9. Experiments on real-world datasets
  10. Conclusion
  11. Numerical results for real-world datasets
  12. Frank-Wolfe algorithm
  13. Implementation details
  14. Normalized fused Gromov-Wasserstein problem
  15. Further implementation details

Key Result

Proposition 1

The tensor-matrix product eq:tensormatrix is of the form with where $\odot$ denotes elementwise multiplication.

Figures (5)

  • Figure 1: Illustration of Subgraph Optimal Transport (SOT).
  • Figure 2: Illustration of Sliding Subgraph Optimal Transport (SSOT).
  • Figure 3: Performance of our algorithms on Erdős–Rényi graphs.
  • Figure 4: Success rates versus query times for different threshold parameters.
  • Figure : Frank-Wolfe method for SOT

Theorems & Definitions (4)

  • Proposition 1: Adaptation of peyre_gromov-wasserstein_2016
  • proof
  • Proposition 2
  • proof : Proof of Proposition \ref{['prop-nFGW']}