# Learning Combinatorial Embedding Networks for Deep Graph Matching

## TL;DR

This paper introduces a deep learning framework for graph matching that learns affinity functions through end-to-end training, capturing higher-order structures and generalizing across different graph sizes and categories.

## Contribution

It proposes a novel combinatorial embedding network that models intra- and cross-graph affinities using deep embeddings, improving matching accuracy and flexibility.

## Key findings

- Outperforms state-of-the-art graph matching methods.
- Effectively captures higher-order structural information.
- Generalizes across different graph sizes and categories.

## Abstract

Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of the node-wise and structure-wise affinity across graphs and the resulting objective, to guide the matching procedure effectively finding the true matching against noises. To this end, this paper devises an end-to-end differentiable deep network pipeline to learn the affinity for graph matching. It involves a supervised permutation loss regarding with node correspondence to capture the combinatorial nature for graph matching. Meanwhile deep graph embedding models are adopted to parameterize both intra-graph and cross-graph affinity functions, instead of the traditional shallow and simple parametric forms e.g. a Gaussian kernel. The embedding can also effectively capture the higher-order structure beyond second-order edges. The permutation loss model is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network allows for varying numbers of nodes in graphs for training and inference. Moreover, our network is class-agnostic with some generalization capability across different categories. All these features are welcomed for real-world applications. Experiments show its superiority against state-of-the-art graph matching learning methods.