Stochastic Iterative Graph Matching

TL;DR

This paper introduces SIGMA, a stochastic iterative model for graph matching that explores a distribution of matchings, refines results incrementally, and outperforms existing methods across various datasets.

Contribution

The paper presents a novel stochastic, iterative graph matching model with dummy nodes, improving accuracy and scalability over prior approaches.

Findings

SIGMA outperforms state-of-the-art models on multiple datasets.

Each component (stochastic training, iterative matching, dummy nodes) improves performance.

The model is scalable and effective for synthetic, biochemistry, and computer vision tasks.

Abstract

Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we propose a new model, Stochastic Iterative Graph MAtching (SIGMA), to address the graph matching problem. Our model defines a distribution of matchings for a graph pair so the model can explore a wide range of possible matchings. We further introduce a novel multi-step matching procedure, which learns how to refine a graph pair's matching results incrementally. The model also includes dummy nodes so that the model does not have to find matchings for nodes without correspondence. We fit this model to data via scalable stochastic optimization. We conduct extensive experiments across synthetic graph datasets as well as biochemistry and computer vision applications. Across all tasks, our results show that SIGMA can produce significantly improved graph matching results compared to state-of-the-art models. Ablation studies verify that each of our components (stochastic training, iterative matching, and dummy nodes) offers noticeable improvement.