Neural Graduated Assignment for Maximum Common Edge Subgraphs

TL;DR

This paper presents Neural Graduated Assignment (NGA), a scalable, unsupervised neural method for solving the Maximum Common Edge Subgraph problem, improving efficiency and performance over traditional approaches.

Contribution

Introduction of NGA, a novel neural, unsupervised method that enhances scalability and effectiveness in solving MCES and related graph matching problems.

Findings

NGA significantly improves computation time on large instances.

NGA outperforms existing methods in graph similarity and retrieval tasks.

Theoretical analysis shows NGA's fast convergence and ability to escape local optima.

Abstract

The Maximum Common Edge Subgraph (MCES) problem is a crucial challenge with significant implications in domains such as biology and chemistry. Traditional approaches, which include transformations into max-clique and search-based algorithms, suffer from scalability issues when dealing with larger instances. This paper introduces ``Neural Graduated Assignment'' (NGA), a simple, scalable, unsupervised-training-based method that addresses these limitations. Central to NGA is stacking of differentiable assignment optimization with neural components, enabling high-dimensional parameterization of the matching process through a learnable temperature mechanism. We further theoretically analyze the learning dynamics of NGA, showing its design leads to fast convergence, better exploration-exploitation tradeoff, and ability to escape local optima. Extensive experiments across MCES computation, graph similarity estimation, and graph retrieval tasks reveal that NGA not only significantly improves computation time and scalability on large instances but also enhances performance compared to existing methodologies. The introduction of NGA marks a significant advancement in the computation of MCES and offers insights into other assignment problems.