Effective Higher-order Link Prediction and Reconstruction from Simplicial Complex Embeddings

In this repository you find code to run experiments of the paper "Effective Higher-order Link Prediction and Reconstruction from Simplicial Complex Embeddings". The library SNAP is needed, together with requirements.txt. The code has been tested with Python 3.6.13.

If you use the code in this repository, please consider citing us:

@inproceedings{piaggesi2022effective,
  title={Effective Higher-order Link Prediction and Reconstruction from Simplicial Complex Embeddings},
  author={Piaggesi, Simone and Panisson, Andr{\'e} and Petri, Giovanni},
  booktitle={Learning on Graphs Conference},
  pages={55--1},
  year={2022},
  organization={PMLR}
}

Repository organization

Description of folders

• processed-data/: datasets downloaded from here and pre-processed (extraction of the largest projected component and filtering of unfrequent nodes). Original data can be downloaded also from here.
• 3way-metrics-data/: 3-way scores computed with this code. We slightly adjusted the Julia code to calculate scores also for the quantiles 0-80 needed in the reconstruction task. You need to download this folder to run the 3-way analysis.

Description of python files

-simplex2hasse.py File got from the reference repo with few modifications for our purposes.

-snap_node2vec.py Utilities to run node2vec with the SNAP library.

-k_simple2vec.py Utilities to run k-simplex2vec, downloaded from the reference repo.

-calibrated_metrics.py Utilities to compute calibrated AUC-PR, downloaded from the reference repo.

-utils.py Utilities for our experiments.

Description of jupyter notebooks

-s2v_train.ipynb and ks2v_train.ipynb Jupyter notebooks to train Simplex2Vec and K-Simplex2Vec.

-negative_hyperedge_sampling.ipynb Jupyter notebook to sample negative hyperedges. You need to set the variable TUPLE_SIZE=3 (or 4) to sample results.

-s2v_dimensions_gridsearch.ipynb and ks2v_dimensions_gridsearch.ipynb Jupyter notebooks needed to find the best dimension scores in order to plot figures.

-3way_figures.ipynb and 3way_figures.ipynb Plot figures with previously computed results.

-4way_tables.ipynb and 4way_tables.ipynb Show results into tables.

References

1. Billings, Jacob Charles Wright, et al. "Simplex2vec embeddings for community detection in simplicial complexes." arXiv preprint arXiv:1906.09068 (2019).
2. Benson, Austin R., et al. "Simplicial closure and higher-order link prediction." Proceedings of the National Academy of Sciences 115.48 (2018): E11221-E11230.
3. Hacker, Celia. "k-simplex2vec: a simplicial extension of node2vec." arXiv preprint arXiv:2010.05636 (2020).
4. Siblini, Wissam, et al. "Master your metrics with calibration." International Symposium on Intelligent Data Analysis. Springer, Cham, 2020.