Graph Encoder Embedding

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This github repo provides a working code for graph encoder embedding, which is updated regularly to reflect our research progress.

The Main folder contains the core GraphEncoder function in three languages:

• MATLAB: GraphEncoder.m
• Python: GraphEncoder.ipynb
• R: GraphEncoder.R

And several extension functions for MATLAB (not yet ported to Python or R):

• GraphCorr.m (Graph correlation between multiple graphs with same vertex label)
• TemporalGraph.m (Temporal GEE for multiple graphs with same vertex label)
• UnsupGraph.m (Unsupervised GEE for graph without vertex label)
• RefinedGEE.m (Refined GEE for improved classification)

The Data folder contains the public real data used in the reference papers.

The Experiments folder contains various experiments, plots, and auxiliary functions for the reference papers.

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Basic Usage in MATLAB:

Given a graph A (either an nn square matrix or an s3 edgelist) and corresponding label vector Y (n*1 vector with K classes), the following outputs the supervised graph encoder embedding

Z=GraphEncoder(A,Y); where Z is the n*K vertex embedding.

Given a time-series graph A (stored in a 1*T cell, and each cell can be either square matrix of edgelist), and a label vector Y, the following outputs the temporal embedding:

[Z,Dynamic]=TemporalGraph(E,Y); where Dynamic contains the vertex, community, and graph dynamic in a 1*3 cell output.

Given a graph A and desired number of class K (or a range), the following outputs the unsupervised embedding:

[Z,Y]=UnsupGraph(A,K); where Z is the unsupervised vertex embedding, and Y is the estimated class label vector for each vertex.

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References:

1. C. Shen and Q. Wang and C. E. Priebe, "One-Hot Graph Encoder Embedding", IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(6):7933 - 7938, 2023. DOI: https://doi.org/10.1109/TPAMI.2022.3225073, arXiv:2109.13098

2. C. Shen and Y. Park and C. E. Priebe, "Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detection", in 2023 2nd International Conference on Algorithms, Data Mining, and Information Technology, pp. 13-18, ACM, 2023. DOI: https://doi.org/10.1145/3625403.3625407, arXiv:2301.11290

3. C. Shen, J. Larson, H. Trinh, X. Qin, Y. Park, and C. E. Priebe, "Discovering Communication Pattern Shifts in Large-Scale Labeled Networks using Encoder Embedding and Vertex Dynamics", IEEE Transactions on Network Science and Engineering, 11(2):2100 - 2109, 2024. DOI: https://doi.org/10.1109/TNSE.2023.3337600, arXiv:2305.02381.

4. C. Shen, C. E. Priebe, J. Larson, H. Trinh, "Synergistic Graph Fusion via Encoder Embedding", Information Sciences, 120912, 2024. DOI: https://doi.org/10.1016/j.ins.2024.120912. arXiv:2303.18051

5. C. Shen, J. Larson, H. Trinh, and C. E. Priebe, "Refined Graph Encoder Embedding via Self-Training and Latent Community Recovery". arXiv:2405.12797

6. C. Shen, J. Arroyo, J. Xiong, and J. T. Vogelstein, "Graph Independence Testing via Encoder Embedding and Community Correlations". arXiv:1906.03661