This is the repository of the paper "Continuous Product Graph Neural Networks" published in the thirty-eighth annual Conference on Neural Information Processing Systems (NeurIPS 2024).
Authors: Aref Einizade, Fragkiskos D. Malliaross, and Jhony H Giraldo.
- Remark: A more organized and completed version of the implementation codes will be provided soon.
Processing multidomain data defined on multiple graphs holds significant potential in various practical applications in computer science. However, current methods are mostly limited to discrete graph filtering operations. Tensorial partial differential equations on graphs (TPDEGs) provide a principled framework for modeling structured data across multiple interacting graphs, addressing the limitations of the existing discrete methodologies. In this paper, we introduce Continuous Product Graph Neural Networks (CITRUS) that emerge as a natural solution to the TPDEG. CITRUS leverages the separability of continuous heat kernels from Cartesian graph products to efficiently implement graph spectral decomposition. We conduct thorough theoretical analyses of the stability and over-smoothing properties of CITRUS in response to domain-specific graph perturbations and graph spectra effects on the performance. We evaluate CITRUS on well-known traffic and weather spatiotemporal forecasting datasets, demonstrating superior performance over existing approaches.
If you have Python's virtualenv package installed (through apt on Ubuntu), you can make a virtual environment via the following:
# change your path and name for your virtual env (remove [])
python3 -m virtualenv ~/path/to/virtual/env/storage/[name]
# then source your environment (you need to do this each time you run!)
# again, remove the [] from name
source ~/path/to/virtual/env/storage/[name]
# this should give a nice `([name])` at the beginning of each terminal linegit clone https://github.com/ArefEinizade2/CITRUS.git Our code requires Python >= 3.11.5
You also need the additional packages listed in the requirements.txt file. You can install the requirements using:
pip install -r requirements.txtWith the requirements installed, the scripts are ready to be run and used. To have a tutorial general demo about how the CITRUS model works, simply run CITRUS_demo.ipynb or:
python3 CITRUS_demo.py- For analyzing the over-smoothing aspect of the CITRUS, in the Oversmoothing_Analysis folder, run Oversmoothing_Analysis.ipynb or:
python3 OverSmoothing_Analysis.py- For analyzing the stability aspect of the CITRUS, in the Stability_Analysis folder, run Stability_Analysis.ipynb and Stability_Analysis_Plot.ipynb or:
python3 Stability_Analysis.py
python3 Stability_Analysis_Plot.py- For generating the results on the MOLENE dataset, in the molene folder, run Molene_prediction.ipynb or:
python3 Molene_prediction.py- For generating the results on the MetrLA dataset, in the MetrLA_PemsBay folder, run MetrLA_Github.ipynb or:
python3 MetrLA_Github.py- Remark: Note that the proposed CITRUS module has been used in different architectures across synthetic and real-world datasets depending on their downstream learning tasks.
If you use our code, please consider citing our work:
@inproceedings{
einizade2024continuous,
title={Continuous Product Graph Neural Networks},
author={Aref Einizade and Fragkiskos D. Malliaros and Jhony H. Giraldo},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=XRNN9i1xpi}
}This work was supported by the center Hi! PARIS and ANR (French National Research Agency) under the JCJC project GraphIA (ANR-20-CE23-0009-01).
- Some segments of the codes heavily rely on the implementation codes of the paper Graph-time convolutional neural networks: Architecture and theoretical analysis and this Github repo.
For any query, please contact me at: aref dot einizade at telecom-paris dot fr