Deep Graph Matching under Quadratic Constraint

TL;DR

This paper introduces a novel deep graph matching method that explicitly incorporates quadratic structural constraints to improve accuracy and reduce ambiguities, demonstrating competitive results on real datasets.

Contribution

The paper proposes a quadratic constraint formulation for deep graph matching, integrating structural information explicitly into the deep learning framework.

Findings

Improved matching accuracy on real-world datasets.

Effective reduction of structural ambiguities.

Enhanced supervision via a false matching loss.

Abstract

Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep graph matching (DGM) methods lies in their ignorance of explicit constraint of graph structures, which may lead the model to be trapped into local minimum in training. In this paper, we propose to explicitly formulate pairwise graph structures as a \textbf{quadratic constraint} incorporated into the DGM framework. The quadratic constraint minimizes the pairwise structural discrepancy between graphs, which can reduce the ambiguities brought by only using the extracted CNN features. Moreover, we present a differentiable implementation to the quadratic constrained-optimization such that it is compatible with the unconstrained deep learning optimizer. To give more precise and proper supervision, a well-designed false matching loss against class imbalance is proposed, which can better penalize the false negatives and false positives with less overfitting. Exhaustive experiments demonstrate that our method competitive performance on real-world datasets.