This repository is the official implementation of Decimated Framelet System on Graphs and Fast G-Framelet Transforms.
The following figure shows the original graph of Minnesota road network and the plots of the decomposed approximation and detail framelet coefficients with a three-level FGT. We set the number of nodes for the sub-graphs as [1000, 300, 100]. To obtain the plots below, you can use the MATLAB script (road_network/exp2.m).
The script (road_network/exp2.m) relies on the graph partitioning algorithm metismex.m for which you have to obtain the C programs from the official website first and then follow the steps in here to compile the C programs in order to call metismex.m directly from MATLAB.
We use FGT to define a spectral graph convolution method, for which we name FGConv. We investigate the effectiveness of FGConv on the graph classification tasks with the composed GNN model FGConv-Sum which has the following architecture: FGConv - FGConv - SumPool - MLP.
To install requirements:
pip install -r requirements.txt
To train and test the model FGConv-Sum in the paper, run the following command. We provide the codes for FGConv-Sum on one of the benchmarks (D&D) from Table 6. The dataset will be downloaded and preprocessed before training. All the experiments were performed using PyTorch Geometric and run on the NVIDIA Tesla V100 GPU with 5,120 CUDA cores and 16GB HBM2 mounted on a high performance computing cluster.
To re-produce the result of FGConv-Sum on graph classification benchmark D&D, we can run:
python fgconv_dd.py
You can change other hyperparameters from the script: batch_size, learning_rate, weight_decay, nhid, epochs, num_high_pass, but we suggest to use the default values for these hyperparameters.
The composed model FGConv-Sum achieves the following performance on graph classification benchmark datasets MUTAG, PROTEINS and D&D. The table below shows the mean test accuracy with SD for 10 repetitions. Compared to existing methods such as GIN, PatchySan, GDCNN and DIffPool, the FGConv-Sum achieves top test accuracy on two of these datasets. The result on D&D can be obtained using the above .py programs. The test results on other benchmarks and comparison with the results of other methods can be seen in the paper.
If you want to cite our paper, please use the citation below:
@article{zheng2020fast,
title={Decimated Framelet System on Graphs and Fast $\mathcal{G}$-Framelet Transforms},
author={Zheng, Xuebin and Zhou, Bingxin and Wang, Yu Guang and Zhuang, Xiaosheng},
booktitle={arXiv preprint arXiv:2012.06922},
year={2020}
}
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