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pygmtools (Python Graph Matching Tools) provides graph matching solvers in Python and is easily accessible via:

$ pip install pygmtools

Official documentation: https://pygmtools.readthedocs.io

Source code: https://github.com/Thinklab-SJTU/pygmtools

Graph matching is a fundamental yet challenging problem in pattern recognition, data mining, and others. Graph matching aims to find node-to-node correspondence among multiple graphs, by solving an NP-hard combinatorial optimization problem.

Doing graph matching in Python used to be difficult, and this library wants to make researchers' lives easier. To highlight, pygmtools has the following features:

• Support various solvers, including traditional combinatorial solvers (including linear, quadratic, and multi-graph) and novel deep learning-based solvers;
• Support various backends, including numpy which is universally accessible, and some state-of-the-art deep learning architectures with GPU support: pytorch, paddle, jittor, tensorflow, mindspore;
• Deep learning friendly, the operations are designed to best preserve the gradient during computation and batched operations support for the best performance.

Installation

You can install the stable release on PyPI:

$ pip install pygmtools

or get the latest version by running:

$ pip install -U https://github.com/Thinklab-SJTU/pygmtools/archive/master.zip # with --user for user install (no root)

Now the pygmtools is available with the numpy backend.

The following packages are required, and shall be automatically installed by pip:

Python >= 3.8
requests >= 2.25.1
scipy >= 1.4.1
Pillow >= 7.2.0
numpy >= 1.18.5
easydict >= 1.7
appdirs >= 1.4.4
tqdm >= 4.64.1
networkx >= 2.8.8
aiohttp
async-timeout

Available Graph Matching Solvers

This library offers user-friendly API for the following solvers:

• Two-Graph Matching Solvers
  • Linear assignment solvers including the differentiable soft Sinkhorn algorithm [1], and the exact solver Hungarian [2].
  • Soft and differentiable quadratic assignment solvers, including spectral graph matching [3] and random-walk-based graph matching [4].
  • Discrete (non-differentiable) quadratic assignment solver integer projected fixed point method [5].
• Multi-Graph Matching Solvers
  • Composition based Affinity Optimization (CAO) solver [6] by optimizing the affinity score, meanwhile gradually infusing the consistency.
  • Multi-Graph Matching based on Floyd shortest path algorithm [7].
  • Graduated-assignment based multi-graph matching solver [8][9] by graduated annealing of Sinkhorn’s temperature.
• Neural Graph Matching Solvers
  • Intra-graph and cross-graph embedding based neural graph matching solvers PCA-GM and IPCA-GM [10] for matching individual graphs.
  • Channel independent embedding (CIE) [11] based neural graph matching solver for matching individual graphs.
  • Neural graph matching solver (NGM) [12] for the general quadratic assignment formulation.
  • Graph edit neural network A-star (GENN-A*) [13] for the graph edit distance problem.

Available Backends

This library is designed to support multiple backends with the same set of API. Please follow the official instructions to install your backend.

The following backends are available:

• Numpy (default backend, CPU only)

• PyTorch (GPU friendly, deep learning friendly)

• Jittor (GPU friendly, JIT support, deep learning friendly)

• PaddlePaddle (GPU friendly, deep learning friendly)

• Tensorflow (GPU friendly, deep learning friendly)

Development status (0.4.2)

	Numpy	PyTorch	Jittor	PaddlePaddle	Tensorflow	MindSpore
Linear Solvers	✔	✔	✔	✔	✔	✔
Classic Solvers	✔	✔	✔	✔	✔	✔
Multi-Graph Solvers	✔	✔	✔	✔	📆	📆
Neural Solvers	✔	✔	✔	✔	📆	📆
Examples Gallery	✔	✔	✔	✔	📆	📆

✔: Supported; 📆: Planned for future versions (contributions welcomed!).

For more details, please read the documentation.

Pretrained Models

The library includes several neural network solvers. The pretrained models shall be automatically downloaded upon needed from Google Drive. If you are experiencing issues accessing Google Drive, please download the pretrained models manually and put them at ~/.cache/pygmtools (for Linux).

Available at: [google drive] [baidu drive]

The Deep Graph Matching Benchmark

pygmtools is also featured with a standard data interface of several graph matching benchmarks. Please read the corresponding documentation for details.

We also maintain a repository containing non-trivial implementation of deep graph matching models, please check out ThinkMatch if you are interested!

Chat with the Community

If you have any questions, or if you are experiencing any issues, feel free to raise an issue on GitHub.

We also offer the following chat rooms if you are more comfortable with them:

• Discord (for English speakers):

  

• QQ Group (for Chinese speakers)/QQ群(中文用户): 696401889

  

Contributing

Any contributions/ideas/suggestions from the community is welcomed! Before starting your contribution, please read the Contributing Guide.

Developers and Maintainers

pygmtools is currently developed and maintained by members from ThinkLab at Shanghai Jiao Tong University.

References

[1] Sinkhorn, Richard, and Paul Knopp. "Concerning nonnegative matrices and doubly stochastic matrices." Pacific Journal of Mathematics 21.2 (1967): 343-348.

[2] Munkres, James. "Algorithms for the assignment and transportation problems." Journal of the Society for Industrial and Applied Mathematics 5.1 (1957): 32-38.

[3] Leordeanu, Marius, and Martial Hebert. "A spectral technique for correspondence problems using pairwise constraints." International Conference on Computer Vision (2005).

[4] Cho, Minsu, Jungmin Lee, and Kyoung Mu Lee. "Reweighted random walks for graph matching." European conference on Computer Vision (2010).

[5] Leordeanu, Marius, Martial Hebert, and Rahul Sukthankar. "An integer projected fixed point method for graph matching and map inference." Advances in Neural Information Processing Systems 22 (2009).

[6] Yan, Junchi, et al. "Multi-graph matching via affinity optimization with graduated consistency regularization." IEEE Transactions on Pattern Analysis and Machine Intelligence 38.6 (2015): 1228-1242.

[7] Jiang, Zetian, Tianzhe Wang, and Junchi Yan. "Unifying offline and online multi-graph matching via finding shortest paths on supergraph." IEEE Transactions on Pattern Analysis and Machine Intelligence 43.10 (2020): 3648-3663.

[8] Solé-Ribalta, Albert, and Francesc Serratosa. "Graduated assignment algorithm for multiple graph matching based on a common labeling." International Journal of Pattern Recognition and Artificial Intelligence 27.01 (2013): 1350001.

[9] Wang, Runzhong, Junchi Yan, and Xiaokang Yang. "Unsupervised Learning of Graph Matching with Mixture of Modes via Discrepancy Minimization." IEEE Transactions on Pattern Analysis and Machine Intelligence 45.8 (2023): 10500-10518.

[10] Wang, Runzhong, Junchi Yan, and Xiaokang Yang. "Combinatorial learning of robust deep graph matching: an embedding based approach." IEEE Transactions on Pattern Analysis and Machine Intelligence 45.6 (2023): 6984-7000.

[11] Yu, Tianshu, et al. "Learning deep graph matching with channel-independent embedding and hungarian attention." International Conference on Learning Representations. 2019.

[12] Wang, Runzhong, Junchi Yan, and Xiaokang Yang. "Neural graph matching network: Learning lawler’s quadratic assignment problem with extension to hypergraph and multiple-graph matching." IEEE Transactions on Pattern Analysis and Machine Intelligence 44.9 (2022): 5261-5279.

[13] Wang, Runzhong, Junchi Yan, and Xiaokang Yang. "Combinatorial Learning of Graph Edit Distance via Dynamic Embedding." IEEE/CVF Conference on Computer Vision and Pattern Recognition (2021): 5241-5250.