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Ensemble Quadratic Assignment Network for Graph Matching

Haoru Tan, Chuang Wang, Sitong Wu, Xu-Yao Zhang, Fei Yin, Cheng-Lin Liu

TL;DR

The paper presents EQAN, a multi-channel GNN for graph matching that ensembles traditional QAP solvers within an end-to-end differentiable framework. By modeling each solver as a channel on the association graph and enabling inter-channel communication via 1×1 convolutions, EQAN achieves robust performance across geometric and semantic matching tasks while maintaining scalability through a random-sampling strategy. The authors establish a differentiable proximal graph matching base, extend it to multi-channel ensembles, and demonstrate strong empirical gains over both traditional methods and prior data-driven approaches, including few-shot 3D shape classification. The approach yields improved robustness to noise, outliers, and rotations, with practical inference times on graphs with thousands of nodes. Theoretical convergence of the proximal solver and extensive ablations support the design choices and scalability claims.

Abstract

Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to feature noises, outlier nodes, and global transformation (e.g.~rotation). In this paper, we propose a graph neural network (GNN) based approach to combine the advantages of data-driven and traditional methods. In the GNN framework, we transform traditional graph-matching solvers as single-channel GNNs on the association graph and extend the single-channel architecture to the multi-channel network. The proposed model can be seen as an ensemble method that fuses multiple algorithms at every iteration. Instead of averaging the estimates at the end of the ensemble, in our approach, the independent iterations of the ensembled algorithms exchange their information after each iteration via a 1x1 channel-wise convolution layer. Experiments show that our model improves the performance of traditional algorithms significantly. In addition, we propose a random sampling strategy to reduce the computational complexity and GPU memory usage, so the model applies to matching graphs with thousands of nodes. We evaluate the performance of our method on three tasks: geometric graph matching, semantic feature matching, and few-shot 3D shape classification. The proposed model performs comparably or outperforms the best existing GNN-based methods.

Ensemble Quadratic Assignment Network for Graph Matching

TL;DR

The paper presents EQAN, a multi-channel GNN for graph matching that ensembles traditional QAP solvers within an end-to-end differentiable framework. By modeling each solver as a channel on the association graph and enabling inter-channel communication via 1×1 convolutions, EQAN achieves robust performance across geometric and semantic matching tasks while maintaining scalability through a random-sampling strategy. The authors establish a differentiable proximal graph matching base, extend it to multi-channel ensembles, and demonstrate strong empirical gains over both traditional methods and prior data-driven approaches, including few-shot 3D shape classification. The approach yields improved robustness to noise, outliers, and rotations, with practical inference times on graphs with thousands of nodes. Theoretical convergence of the proximal solver and extensive ablations support the design choices and scalability claims.

Abstract

Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to feature noises, outlier nodes, and global transformation (e.g.~rotation). In this paper, we propose a graph neural network (GNN) based approach to combine the advantages of data-driven and traditional methods. In the GNN framework, we transform traditional graph-matching solvers as single-channel GNNs on the association graph and extend the single-channel architecture to the multi-channel network. The proposed model can be seen as an ensemble method that fuses multiple algorithms at every iteration. Instead of averaging the estimates at the end of the ensemble, in our approach, the independent iterations of the ensembled algorithms exchange their information after each iteration via a 1x1 channel-wise convolution layer. Experiments show that our model improves the performance of traditional algorithms significantly. In addition, we propose a random sampling strategy to reduce the computational complexity and GPU memory usage, so the model applies to matching graphs with thousands of nodes. We evaluate the performance of our method on three tasks: geometric graph matching, semantic feature matching, and few-shot 3D shape classification. The proposed model performs comparably or outperforms the best existing GNN-based methods.
Paper Structure (46 sections, 3 theorems, 46 equations, 10 figures, 6 tables, 4 algorithms)

This paper contains 46 sections, 3 theorems, 46 equations, 10 figures, 6 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Traditional graph matching algorithms
  4. Data-driven graph matching models
  5. Applications
  6. Graph Matching and Differentiable Solver
  7. Problem formulation
  8. Differentiable proximal graph matching
  9. General differentiable iterative solver
  10. QAP-Solver as a single-channel GNN
  11. Ensemble Quadratic Assignment Model
  12. Initialization module
  13. Ensemble assignment module
  14. The decision layer
  15. Ensemble model as a graph neural network
  16. ...and 31 more sections

Key Result

lemma thmcounterlemma

There exist a constant $\alpha >0$ such that for all $\boldsymbol{z}_{t+1}$, $\boldsymbol{z}_t$ generated during the forward pass of the solver, we have where $D$ is the KL-divergence.

Figures (10)

  • Figure 1: The association graph $\mathcal{G}=(\mathcal{V}, \mathcal{E})$ of two base graphs $G_1=(V_1,E_1)$ and $G_2=({V}_2, {E}_2)$. Each association-node from the association graph represents a candidate matching between a pair of nodes from two base graphs. Graph matching is equivalent to selecting a set of nodes in the association graph RRWMLCSGMNGM with certain exclusive constraints.
  • Figure 2: The ensemble quadratic assignment model consists of three modules. The initialization module computes the affinity matrix and initializes the iteration feature tensor. The ensemble assignment module is a sequence of ensemble blocks, which include a set of classical QAP solvers. Details are shown in Figure \ref{['flow_chart']}. The final layer takes the features created by all previous blocks as input and outputs a matching decision.
  • Figure 3: An Ensemble Block includes a set of QAP-solvers that update the channels of feature independently, and a $1\times 1$ convolution layer that promotes information exchange across the channels.
  • Figure 4: Robustness to noise, outliers, and random rotation. (a) The noise level $\sigma$ changes from 0.0 to 0.2, with $n_\text{in} = 50$, and $n_\text{out} = 0$. (b) We add a number of outliers $n_\text{out}$ from $0$ to $50$ with $n_\text{in} = 35$, and $\sigma = 0.1$. (c) The maximum rotational angle ranges from $0$ to $90$ with $n_\text{in} = 30$, $n_\text{out} = 15$, and $\sigma = 0.1$.
  • Figure 5: Robustness of matching accuracy to random rotations. Left/right bar shows the accuracy on the original/rotated data respectively in each method. Traditional solvers is robust to global rotation but less accurate, whereas existing GNN methods improves the accuracy noticeably but they are very sensitive to global rotations. Our methods (DPGM-net and EQAN) inherit the advantages of both sides.
  • ...and 5 more figures

Theorems & Definitions (4)

  • lemma thmcounterlemma
  • proposition thmcounterproposition
  • lemma thmcounterlemma
  • proof