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Directional diffusion models

Run Yang1, Yuling Yang1, Fan Zhou1, Qiang Sun2
1Shanghai University of Finance and Economics, 2University of Toronto

We introduce a novel class of models termed directional diffusion models (DDM), which adopt data-dependent, anisotropic, and directional noises in the forward diffusion process. This code is an implementation of DDM on 12 public graph datasets.

Graph classification datasets

  • IMDB-B
  • IMDB-M
  • COLLAB
  • REDDIT-B
  • PROTEINS
  • MUTAG

Node classification datasets

  • CORA
  • Citeseer
  • PubMed
  • Ogbn-arxiv
  • Amazon-Computer
  • Amazon-Photo

Framework

framework

Usage

conda create -n ddm python=3.8
conda activate ddm
cd ddm-nni
pip install -r requirements.txt

cd to EXP path(MUTAG for example)

cd GraphExp
python main_graph.py --yaml_dir ./yamls/MUTAG.yaml

In view of the sensitivity of diffusion method to hyperparameters, it is recommended to use hyperparameter search methods like NNI to achieve better results Trust me ! In this way, you can achieve better results than what is presented in the paper

Performance

Directional noise v.s. white noise

noise

Graph classification(F1-score)

IMDB-B IMDB-M COLLAB REDDIT-B PROTEINS MUTAG
GIN[1] 75.1±5.1 52.3±2.8 80.2±1.9 92.4±2.5 76.2±2.8 89.4±5.6
DiffPool[2] 72.6±3.9 - 78.9±2.3 92.1±2.6 75.1±2.3 85.0±10.3
Infograph[3] 73.03±0.87 49.69±0.53 70.65±1.13 82.50±1.42 74.44±0.31 89.01±1.13
GraphCL[4] 71.14±0.44 48.58±0.67 71.36±1.15 89.53±0.84 74.39±0.45 86.80±1.34
JOAO[5] 70.21±3.08 49.20±0.77 69.50±0.36 85.29±1.35 74.55±0.41 87.35±1.02
GCC[6] 72 49.4 78.9 89.8 - -
MVGRL[7] 74.20±0.70 51.20±0.50 - 84.50±0.60 - 89.70±1.10
GraphMAE[8] 75.52±0.66 51.63±0.52 80.32±0.46 88.01±0.19 75.30±0.39 88.19±1.26
DDM 76.40±0.22 52.53±0.31 81.72±0.31 89.15±1.3 75.74±0.50 91.51±1.45

Node classification(F1-score)

Dataset Cora Citeseer PubMed Ogbn-arxiv Computer Photo
GAT 83.0 ± 0.7 72.5 ± 0.7 79.0 ± 0.3 72.10 ± 0.13 86.93 ± 0.29 92.56 ± 0.35
DGI[9] 82.3 ± 0.6 71.8 ± 0.7 76.8 ± 0.6 70.34 ± 0.16 83.95 ± 0.47 91.61 ± 0.22
MVGRL[7] 83.5 ± 0.4 73.3 ± 0.5 80.1 ± 0.7 - 87.52 ± 0.11 91.74 ± 0.07
BGRL[10] 82.7 ± 0.6 71.1 ± 0.8 79.6 ± 0.5 71.64 ± 0.12 89.68 ± 0.31 92.87 ± 0.27
InfoGCL[11] 83.5 ± 0.3 73.5 ± 0.4 79.1 ± 0.2 - - -
CCA-SSG[12] 84.0 ± 0.4 73.1 ± 0.3 81.0 ± 0.4 71.24 ± 0.20 88.74 ± 0.28 93.14 ± 0.14
GPT-GNN[13] 80.1 ± 1.0 68.4 ± 1.6 76.3 ± 0.8 - - -
GraphMAE[8] 84.2 ± 0.4 73.4 ± 0.4 81.1 ± 0.4 71.75 ± 0.17 88.63 ± 0.17 93.63 ± 0.22
DDM 83.4±0.2 74.3±0.3 81.7±0.8 71.29±0.18 90.56±0.21 95.09±0.18

Citations

[1]:Xu, K., Hu, W., Leskovec, J., and Jegelka, S. (2018). How powerful are graph neural networks? arXiv preprint arXiv:1810.00826.
[2]:Ying, Z., You, J., Morris, C., Ren, X., Hamilton, W., and Leskovec, J. (2018). Hierarchical graph representation learning with differentiable pooling. Advances in neural information processing systems, 31.
[3]:Sun, F.-Y., Hoffmann, J., Verma, V., and Tang, J. (2019). Infograph: Unsupervised and semi- supervised graph-level representation learning via mutual information maximization. arXiv preprint arXiv:1908.01000.
[4]:You, Y., Chen, T., Sui, Y., Chen, T., Wang, Z., and Shen, Y. (2020). Graph contrastive learning with augmentations. Advances in neural information processing systems, 33:5812–5823.
[5]:You, Y., Chen, T., Shen, Y., and Wang, Z. (2021). Graph contrastive learning automated. In International Conference on Machine Learning, pages 12121–12132. PMLR.
[6]:Qiu, J., Chen, Q., Dong, Y., Zhang, J., Yang, H., Ding, M., Wang, K., and Tang, J. (2020). Gcc: Graph contrastive coding for graph neural network pre-training. In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pages 1150–1160.
[7]:Hassani, K. and Khasahmadi, A. H. (2020). Contrastive multi-view representation learning on graphs. In International conference on machine learning, pages 4116–4126. PMLR.
[8]:Hou, Z., Liu, X., Dong, Y., Wang, C., Tang, J., et al. (2022). Graphmae: Self-supervised masked graph autoencoders. arXiv preprint arXiv:2205.10803.
[9]:Velickovic, P., Fedus, W., Hamilton, W. L., Liò, P., Bengio, Y., and Hjelm, R. D. (2019). Deep graph infomax. ICLR (Poster), 2(3):4.
[10]:Thakoor, S., Tallec, C., Azar, M. G., Azabou, M., Dyer, E. L., Munos, R., Veliˇckovi ́c, P., and Valko, M. (2021). Large-scale representation learning on graphs via bootstrapping. arXiv preprint arXiv:2102.06514.
[11]:Xu, D., Cheng, W., Luo, D., Chen, H., and Zhang, X. (2021). Infogcl: Information-aware graph contrastive learning. Advances in Neural Information Processing Systems, 34:30414–30425.
[12]:Zhang, H., Wu, Q., Yan, J., Wipf, D., and Yu, P. S. (2021). From canonical correlation analysis to self-supervised graph neural networks. Advances in Neural Information Processing Systems, 34:76–89.
[13]:Hu, Z., Dong, Y., Wang, K., Chang, K.-W., and Sun, Y. (2020b). Gpt-gnn: Generative pre-training of graph neural networks. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 1857–1867.

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