This repository is the official implementation of How Framelets Enhance Graph Neural Networks.
The above figure shows framelet convolution (UFGConv): given a graph with structure (adjacency matrix) and feature information, the target is to properly embed the graph by graph convolution. The demonstrative sample is a graph with 10 nodes and 3 features extracted from PROTEINS in TUDataset. The framelet dilation and scale level are both set to default value 2. The UFGConv applies tensor-based framelet transform, and constructs one low-pass and two high-pass framelet transform matrices, which are then multiplied by the input feature matrix to produce the framelet coefficients. Moreover, these coefficients are processed by the trainable network filter and compressed by the shrinkage. Finally, the activated coefficients are reconstructed and sent back to the spatial domain as the convolution output by using the framelet transform matrices again with transposed alignment.
The above figure shows framelet pooling (UFGPool-Sum or UFGPool-Spectrum): the three framelet transform matrices are retrieved from the figure for framelet convolution with the same protein sample and parameter setting. The scale-wise framelet coefficients are aggregated to three vectors by sum or sum of squares (framelet spectrum). The (1 low pass and 2 high passes) vectors are then concatenated as the readout for the classifier.
To install requirements:
pip install -r requirements.txt
To reproduce the results in Table 1 of the main text, you can use the following command
python UFGConv_relu.py --dataset Cora
for ReLU model. To reproduce the results for shrinkage model, please run the following script.
python UFGConv_shrinkage.py --dataset Cora
The above two commands are for Cora. To reproduce the experiment results for the other datasets, you can change the argument of --dataset to Citeseer or Pubmed. Other hyperparameters include: --lr, --wd, --nhid, --Lev, --s, --dropout. Please note that the default values of these hyperparameters are only for Cora.
To reproduce the results in Table 3 of the main text, you can use the following command:
python UFGPool.py --dataset PROTEINS
Other hyperparameters include: --lr, --wd, --nhid, --Lev, --s, --dropout.
If you consider our codes and datasets useful, please cite:
@inproceedings{zheng2021how,
title={How Framelets Enhance Graph Neural Networks},
author={Zheng, Xuebin and Zhou, Bingxin and Gao, Junbin and Wang, Yu Guang and Lio, Pietro and Li, Ming and Montufar, Guido},
booktitle={ICML},
year={2021}
}
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