Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Neural Graduated Assignment for Maximum Common Edge Subgraphs

Chaolong Ying, Yingqi Ruan, Xuemin Chen, Yaomin Wang, Tianshu Yu

TL;DR

This paper tackles the NP-hard Maximum Common Edge Subgraph (MCES) problem by introducing Neural Graduated Assignment (NGA), a scalable, unsupervised neural framework. NGA builds an Association Common Graph to recast MCES as a Quadratic Assignment Problem and optimizes it through iterative, differentiable refinement with a learnable temperature schedule, enabling effective exploration and rapid convergence. The authors provide theoretical insights into NGA’s dynamics and demonstrate major performance gains in MCES computation, graph similarity estimation, and graph retrieval on large molecular graphs, including substantial runtime reductions. The approach delivers explicit MCES structures, improves scalability beyond traditional search-based methods, and offers a versatile framework potentially applicable to broader assignment problems.

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.

Neural Graduated Assignment for Maximum Common Edge Subgraphs

TL;DR

This paper tackles the NP-hard Maximum Common Edge Subgraph (MCES) problem by introducing Neural Graduated Assignment (NGA), a scalable, unsupervised neural framework. NGA builds an Association Common Graph to recast MCES as a Quadratic Assignment Problem and optimizes it through iterative, differentiable refinement with a learnable temperature schedule, enabling effective exploration and rapid convergence. The authors provide theoretical insights into NGA’s dynamics and demonstrate major performance gains in MCES computation, graph similarity estimation, and graph retrieval on large molecular graphs, including substantial runtime reductions. The approach delivers explicit MCES structures, improves scalability beyond traditional search-based methods, and offers a versatile framework potentially applicable to broader assignment problems.

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.
Paper Structure (49 sections, 7 theorems, 60 equations, 15 figures, 6 tables, 2 algorithms)

This paper contains 49 sections, 7 theorems, 60 equations, 15 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Efforts on Solving MCS.
  4. Efforts on Graph Similarity Computation and Graph Retrieval.
  5. Preliminary
  6. Maximum Common Edge Subgraph.
  7. Quadratic Assignment Problem.
  8. Methodology
  9. Overview
  10. Unsupervised Training of MCES
  11. ACG for Learning the Correspondences
  12. Neural Graduated Assignment
  13. Gumbel Sampling for Optimization
  14. Theoretical Analysis
  15. Experiments
  16. ...and 34 more sections

Key Result

Proposition 1

Denote the node set of $G_1 \Diamond G_2$ as $\mathcal{V}_{\Diamond} = \{(u, v)| u \in \mathcal{V}(G_1), v \in \mathcal{V}(G_2)\}$. Consider a set of subgraphs of $G_1 \Diamond G_2$ where each node of $G_1$ and $G_2$ is selected at most once, i.e. any two nodes $(u_i, v_i)$ and $(u_j, v_j)$ in this

Figures (15)

  • Figure 1: For two labeled graphs (molecules), the maximum common edge subgraph (MCES) is highlighted in circle and the node correspondences are encoded in arrowed lines.
  • Figure 2: An overview of Neural Graduated Assignment.
  • Figure 3: Visualization of MCES with NGA. Matched atoms and bonds are highlighted in red, with circles of the same color indicating correspondences.
  • Figure 4: Results of Accuracy $(\%)$$\uparrow$ for MCES.
  • Figure 5: Results of MSE ($\times 10^{-3}$) $\downarrow$ for graph similarity.
  • ...and 10 more figures

Theorems & Definitions (12)

  • Proposition 1
  • Theorem 1
  • Proposition 2
  • Definition 1
  • Proposition 2
  • proof
  • Proposition 2
  • proof
  • Lemma 1
  • proof
  • ...and 2 more