Multi-view Graph Condensation via Tensor Decomposition

May 12, 2026 · View on GitHub

This repository is the official PyTorch implementation of "Multi-view Graph Condensation via Tensor Decomposition", published in the Proceedings of the Nineteenth ACM International Conference on Web Search and Data Mining (WSDM 2026).

Paper Link: https://dl.acm.org/doi/10.1145/3773966.3777968

Requirements

This code was implemented using Python 3.11.5 and the following packages:

  • dotmap==1.3.30
  • faiss==1.9.0
  • gdown==5.2.0
  • ogb==1.3.6
  • scikit-learn==1.6.1
  • scipy==1.13.1
  • tensorly==0.9.0
  • torch==2.1.2
  • torch-geometric==2.6.1
  • wandb==0.19.6

Datasets

The following datasets are supported:

  • cora
  • citeseer
  • pubmed
  • ogbn-arxiv
  • flickr
  • reddit

Cora, Citeseer, Pubmed, and Ogbn-arxiv are automatically downloaded when running the code.

For Flickr and Reddit, we use the versions provided by GraphSAINT. They are available at:

After downloading Flickr and Reddit, place them in the appropriate dataset directory used by the repository.

How to run the code

The main script is:

python src/train.py --dataset <dataset_name> --reduction_rate <reduction_rate>

For example, to run GCTD on Cora with a 1.3% condensation ratio:

python src/train.py --dataset cora --reduction_rate 0.013

You can also manually set the main hyperparameters:

python src/train.py \
  --dataset cora \
  --reduction_rate 0.013 \
  --R 5 \
  --add_ratio 0.1 \
  --drop_ratio 0.1 \
  --rec_epochs 200 \
  --gnn_epochs 600 \
  --hidden_dim 256 \
  --gnn gcn \
  --lr_rec 0.001 \
  --lr_gnn 0.001 \
  --wd 0.001 \
  --wd_gnn 0.001 \
  --bsz 1024 \
  --use_kmeans 1 \
  --cuda

Hyperparameter search with Weights & Biases

We used Weights & Biases (wandb) to perform hyperparameter search. An example sweep configuration is provided in:

wandb_example.yml

To launch a sweep, run:

wandb sweep wandb_example.yml

Then start an agent using the command printed by W&B, for example:

wandb agent <entity>/<project>/<sweep_id>

The user can either use the provided sweep file, create their own sweep file, or manually set any parameter through the command line.

Main arguments

The following arguments can be modified when running src/train.py.

Dataset and reduction

  • --dataset

    Dataset used in the experiment. Available options are cora, citeseer, pubmed, ogbn-arxiv, flickr, and reddit.

  • --reduction_rate

    Condensation ratio used to define the size of the synthetic graph.

  • --rec_epochs

    Number of epochs used to optimize the tensor decomposition.

    Default: 200

  • --R

    Number of graph views/tensor slices. When R=1, the method reduces to the single-view matrix tri-factorization setting.

    Default: 5

  • --add_ratio

    Percentage of random edges added when generating augmented graph views.

    Default: 0.1

  • --drop_ratio

    Percentage of edges randomly removed when generating augmented graph views.

    Default: 0.1

  • --lr_rec

    Learning rate used during the reconstruction/decomposition step.

    Default: 0.001

  • --wd

    Weight decay used during the reconstruction/decomposition step.

    Default: 0.001

  • --bsz

    Batch size used during the decomposition step.

    Default: 1024

  • --atol

    Absolute tolerance used as a convergence criterion for the reconstruction loss.

    Default: 1e-7

  • --weighted

    Determines whether the values from the learned core tensor are used as edge weights in the condensed graph.

    Default: 1

  • --use_kmeans

    Uses K-Means on the learned factor matrix to assign original nodes to synthetic nodes.

    Default: 1

  • --kmeans_redo

    Number of K-Means restarts.

    Default: 1

  • --kmeans_iter

    Number of K-Means iterations.

    Default: 20

GNN evaluation parameters

  • --gnn_epochs

    Number of epochs used to train the GNN on the condensed graph.

    Default: 600

  • --gnn

    GNN architecture used for evaluation.

    Default: gcn

  • --hidden_dim

    Hidden dimension of the GNN.

    Default: 256

  • --dropout

    Dropout used during GNN training.

    Default: 0.0

  • --lr_gnn

    Learning rate used during GNN training.

    Default: 0.001

  • --wd_gnn

    Weight decay used during GNN training.

    Default: 0.001

Runtime options

  • --cuda

    Enables GPU training when available.

    Default: enabled

  • --gpu_id

    GPU ID used for training.

    Default: 0

  • --verbose

    Prints additional information during execution.

    Default: enabled

  • --use_cached

    Uses cached files (e.g., multi-view tensors) when available.

    Default: enabled

Reference

If you use this code, please cite our paper:

@inproceedings{10.1145/3773966.3777968,
author = {Roque dos Santos, Nicolas and Ahn, Dawon and Minatel, Diego and de Andrade Lopes, Alneu and Papalexakis, Evangelos},
title = {Multi-view Graph Condensation via Tensor Decomposition},
year = {2026},
isbn = {9798400722929},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3773966.3777968},
doi = {10.1145/3773966.3777968},
booktitle = {Proceedings of the Nineteenth ACM International Conference on Web Search and Data Mining},
pages = {563–573},
numpages = {11},
keywords = {graph condensation, tensor decomposition, graph neural networks, matrix tri-factorization},
location = {USA},
series = {WSDM '26}
}