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Scaling Graph Neural Networks with Approximate PageRank

Published:20 August 2020Publication History

ABSTRACT

Graph neural networks (GNNs) have emerged as a powerful approach for solving many network mining tasks. However, learning on large graphs remains a challenge -- many recently proposed scalable GNN approaches rely on an expensive message-passing procedure to propagate information through the graph. We present the PPRGo model which utilizes an efficient approximation of information diffusion in GNNs resulting in significant speed gains while maintaining state-of-the-art prediction performance. In addition to being faster, PPRGo is inherently scalable, and can be trivially parallelized for large datasets like those found in industry settings.

We demonstrate that PPRGo outperforms baselines in both distributed and single-machine training environments on a number of commonly used academic graphs. To better analyze the scalability of large-scale graph learning methods, we introduce a novel benchmark graph with 12.4 million nodes, 173 million edges, and 2.8 million node features. We show that training PPRGo from scratch and predicting labels for all nodes in this graph takes under 2 minutes on a single machine, far outpacing other baselines on the same graph. We discuss the practical application of PPRGo to solve large-scale node classification problems at Google.

References

  1. S. Abu-El-Haija, A. Kapoor, B. Perozzi, and J. Lee. 2018. N-gcn: multi-scale graph convolution for semi-supervised node classification. arXiv preprint arXiv:1802.08888.Google ScholarGoogle Scholar
  2. S. Abu-El-Haija et al. 2019. MixHop: higher-order graph convolutional architectures via sparsified neighborhood mixing. ICML, 21--29.Google ScholarGoogle Scholar
  3. R. Andersen, C. Borgs, J. T. Chayes, J. E. Hopcroft, V. S. Mirrokni, and S.-H. Teng. 2008. Local computation of pagerank contributions. Internet Mathematics, 5, 23--45.Google ScholarGoogle ScholarCross RefCross Ref
  4. R. Andersen, F. Chung, and K. Lang. 2006. Local graph partitioning using pagerank vectors. FOCS, 475--486.Google ScholarGoogle Scholar
  5. P. W. Battaglia et al. 2018. Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261.Google ScholarGoogle Scholar
  6. A. Bojchevski and S. Günnemann. 2018. Deep gaussian embedding of graphs: unsupervised inductive learning via ranking.Google ScholarGoogle Scholar
  7. P. Boldi, V. Lonati, M. Santini, and S. Vigna. 2006. Graph fibrations, graph isomorphism, and pagerank. RAIRO Theor. Informatics Appl., 40, 2, 227--253.Google ScholarGoogle ScholarCross RefCross Ref
  8. J. Bruna, W. Zaremba, A. Szlam, and Y. LeCun. 2013. Spectral networks and locally connected networks on graphs. arXiv preprint arXiv:1312.6203.Google ScholarGoogle Scholar
  9. E. Buchnik and E. Cohen. 2018. Bootstrapped graph diffusions: exposing the power of nonlinearity. SIGMETRICS, 8--10.Google ScholarGoogle Scholar
  10. C. Chambers, A. Raniwala, F. Perry, S. Adams, R. R. Henry, R. Bradshaw, and N. Weizenbaum. 2010. Flumejava: easy, efficient data-parallel pipelines. ACM Sigplan Notices, 45, 6, 363--375.Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. I. Chami, S. Abu-El-Haija, B. Perozzi, C. Ré, and K. Murphy. 2020. Machine learning on graphs: a model and comprehensive taxonomy. arXiv preprint arXiv:2005.03675.Google ScholarGoogle Scholar
  12. J. Chen, J. Zhu, and L. Song. 2018. Stochastic training of graph convolutional networks with variance reduction. ICML, 941--949.Google ScholarGoogle Scholar
  13. J. Chen, T. Ma, and C. Xiao. 2018. Fastgcn: fast learning with graph convolutional networks via importance sampling. arXiv preprint arXiv:1801.10247.Google ScholarGoogle Scholar
  14. Z. Chen, L. Li, and J. Bruna. 2018. Supervised community detection with line graph neural networks.Google ScholarGoogle Scholar
  15. W. Chiang, X. Liu, S. Si, Y. Li, S. Bengio, and C. Hsieh. 2019. Cluster-gcn: an efficient algorithm for training deep and large graph convolutional networks. KDD. ACM, 257--266.Google ScholarGoogle Scholar
  16. M. Defferrard, X. Bresson, and P. Vandergheynst. 2016. Convolutional neural networks on graphs with fast localized spectral filtering. Advances in Neural Information Processing Systems, 3844--3852.Google ScholarGoogle Scholar
  17. M. Fey and J. E. Lenssen. 2019. Fast graph representation learning with pytorch geometric. CoRR, abs/1903.02428. arXiv: 1903.02428.Google ScholarGoogle Scholar
  18. D. Fogaras and B. Rácz. 2004. Towards scaling fully personalized pagerank. WAW.Google ScholarGoogle Scholar
  19. Y. Fujiwara, M. Nakatsuji, H. Shiokawa, T. Mishima, and M. Onizuka. 2013. Fast and exact top-k algorithm for pagerank. AAAI.Google ScholarGoogle Scholar
  20. H. Gao, Z. Wang, and S. Ji. 2018. Large-scale learnable graph convolutional networks. KDD, 1416--1424.Google ScholarGoogle Scholar
  21. J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl. 2017. Neural message passing for quantum chemistry. arXiv preprint arXiv:1704.01212.Google ScholarGoogle Scholar
  22. D. F. Gleich, K. Kloster, and H. Nassar. 2015. Localization in seeded pagerank. arXiv preprint arXiv:1509.00016.Google ScholarGoogle Scholar
  23. M. Gori, G. Monfardini, and F. Scarselli. 2005. A new model for learning in graph domains. IJCNN, 729--734.Google ScholarGoogle Scholar
  24. W. Hamilton, Z. Ying, and J. Leskovec. 2017. Inductive representation learning on large graphs. Advances in Neural Information Processing Systems, 1024--1034.Google ScholarGoogle Scholar
  25. K. He, X. Zhang, S. Ren, and J. Sun. 2016. Deep Residual Learning for Image Recognition. CVPR, 770--778.Google ScholarGoogle Scholar
  26. W. Huang, T. Zhang, Y. Rong, and J. Huang. 2018. Adaptive sampling towards fast graph representation learning. Advances in Neural Information Processing Systems, 4563--4572.Google ScholarGoogle Scholar
  27. G. Jeh and J. Widom. 2003. Scaling personalized web search. WWW.Google ScholarGoogle Scholar
  28. A. Kannan et al. 2016. Smart reply: automated response suggestion for email. KDD, 955--964.Google ScholarGoogle Scholar
  29. G. Karypis and V. Kumar. 1998. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on scientific Computing, 20, 1.Google ScholarGoogle Scholar
  30. D. P. Kingma and J. Ba. 2014. Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980.Google ScholarGoogle Scholar
  31. T. N. Kipf and M. Welling. 2016. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907.Google ScholarGoogle Scholar
  32. J. Gasteiger, A. Bojchevski, and S. Günnemann. 2019. Predict then propagate: graph neural networks meet personalized pagerank. ICLR.Google ScholarGoogle Scholar
  33. Q. Li, Z. Han, and X.-M. Wu. 2018. Deeper insights into graph convolutional networks for semi-supervised learning. arXiv preprint arXiv:1801.07606.Google ScholarGoogle Scholar
  34. P. Lofgren, S. Banerjee, and A. Goel. 2016. Personalized pagerank estimation and search: a bidirectional approach. WSDM.Google ScholarGoogle Scholar
  35. H. Nassar, K. Kloster, and D. F. Gleich. 2015. Strong localization in personalized pagerank vectors. International Workshop on Algorithms and Models for the Web-Graph. Springer, 190--202.Google ScholarGoogle Scholar
  36. M. Niepert, M. Ahmed, and K. Kutzkov. 2016. Learning convolutional neural networks for graphs. ICML, 2014--2023.Google ScholarGoogle Scholar
  37. L. Page, S. Brin, R. Motwani, and T. Winograd. 1998. The pagerank citation ranking: bringing order to the web.Google ScholarGoogle Scholar
  38. B. Perozzi, M. Schueppert, J. Saalweachter, and M. Thakur. 2016. When recommendation goes wrong: anomalous link discovery in recommendation networks. KDD, 569--578.Google ScholarGoogle Scholar
  39. S. Ravi. 2016. Graph-powered machine learning at google. https://ai.googleblog. com/2016/10/graph-powered-machine-learning-at-google.html. (2016).Google ScholarGoogle Scholar
  40. R. Al-Rfou, D. Zelle, and B. Perozzi. 2019. Ddgk: learning graph representations for deep divergence graph kernels. WWW, 37--48.Google ScholarGoogle Scholar
  41. R. Sato, M. Yamada, and H. Kashima. 2019. Constant time graph neural networks. arXiv preprint arXiv:1901.07868.Google ScholarGoogle Scholar
  42. F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini. 2009. The graph neural network model. IEEE Transactions on Neural Networks, 20, 1.Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. A. Sinha, Z. Shen, Y. Song, H. Ma, D. Eide, B.-J. P. Hsu, and K. Wang. 2015. An overview of microsoft academic service (mas) and applications. WWW 2015.Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. P. Velickovic, G. Cucurull, A. Casanova, A. Romero, P. Lio, and Y. Bengio. 2017. Graph attention networks. arXiv preprint arXiv:1710.10903, 1, 2.Google ScholarGoogle Scholar
  45. S. Wang, Y. Tang, X. Xiao, Y. Yang, and Z. Li. 2016. Hubppr: effective indexing for approximate personalized pagerank. PVLDB, 10, 205--216.Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. S. Wang, R. Yang, X. Xiao, Z. Wei, and Y. Yang. 2017. Fora: simple and effective approximate single-source personalized pagerank. KDD.Google ScholarGoogle Scholar
  47. X. Wang, A. Shakery, and T. Tao. 2005. Dirichlet pagerank. SIGIR.Google ScholarGoogle Scholar
  48. Z. Wei, X. He, X. Xiao, S. Wang, S. Shang, and J.-R. Wen. 2018. Topppr: topk personalized pagerank queries with precision guarantees on large graphs. SIGMOD.Google ScholarGoogle Scholar
  49. F. Wu, T. Zhang, A. H. d. Souza Jr, C. Fifty, T. Yu, and K. Q. Weinberger. 2019. Simplifying graph convolutional networks. arXiv preprint arXiv:1902.07153.Google ScholarGoogle Scholar
  50. Z. Wu, S. Pan, F. Chen, G. Long, C. Zhang, and P. S. Yu. 2019. A comprehensive survey on graph neural networks. arXiv preprint arXiv:1901.00596.Google ScholarGoogle Scholar
  51. K. Xu, W. Hu, J. Leskovec, and S. Jegelka. 2018. How powerful are graph neural networks? arXiv preprint arXiv:1810.00826.Google ScholarGoogle Scholar
  52. K. Xu, C. Li, Y. Tian, T. Sonobe, K.-i. Kawarabayashi, and S. Jegelka. 2018. Representation learning on graphs with jumping knowledge networks. arXiv preprint arXiv:1806.03536.Google ScholarGoogle Scholar
  53. J. Yang and J. Leskovec. 2015. Defining and evaluating network communities based on ground-truth. Knowledge and Information Systems, 42, 1, 181--213.Google ScholarGoogle ScholarDigital LibraryDigital Library
  54. R. Ying, R. He, K. Chen, P. Eksombatchai, W. L. Hamilton, and J. Leskovec. 2018. Graph convolutional neural networks for web-scale recommender systems. arXiv preprint arXiv:1806.01973.Google ScholarGoogle Scholar
  55. M. Zhang and Y. Chen. 2018. Link prediction based on graph neural networks. arXiv preprint arXiv:1802.09691.Google ScholarGoogle Scholar

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