# PA-GM: Position-Aware Learning of Embedding Networks for Deep Graph Matching

arXiv: https://arxiv.org/abs/2301.01932 · HTML: https://mlsanity.com/paper/2301.01932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 5 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Cross-lingual Knowledge Graph Alignment via Graph Matching Neural Network](https://mlsanity.com/paper/1905.11605/) (2019)

## Abstract (arXiv)

Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential ambiguities present due to nodes and edges with high similarity, and there is a need to find accurate results for similar content matching. In this paper, we introduce a novel end-to-end neural network that can map the linear assignment problem into a high-dimensional space augmented with node-level relative position information, which is crucial for improving the method's performance for similar content matching. Our model constructs the anchor set for the relative position of nodes and then aggregates the feature information of the target node and each anchor node based on a measure of relative position. It then learns the node feature representation by integrating the topological structure and the relative position information, thus realizing the linear assignment between the two graphs. To verify the effectiveness and generalizability of our method, we conduct graph matching experiments, including cross-category matching, on different real-world datasets. Comparisons with different baselines demonstrate the superiority of our method. Our source code is available under https://github.com/anonymous.