ABSTRACT
Graph neural networks (GNNs) have been widely used to learn node representations from graph data in an unsupervised way for downstream tasks. However, when applied to detect anomalies (e.g., outliers, unexpected density), they deliver unsatisfactory performance as existing loss functions fail. For example, any loss based on random walk (RW) algorithms would no longer work because the assumption that anomalous nodes were close with each other could not hold. Moreover, the nature of class imbalance in anomaly detection tasks brings great challenges to reduce the prediction error. In this work, we propose a novel loss function to train GNNs for anomaly-detectable node representations. It evaluates node similarity using global grouping patterns discovered from graph mining algorithms. It can automatically adjust margins for minority classes based on data distribution. Theoretically, we prove that the prediction error is bounded given the proposed loss function. We empirically investigate the GNN effectiveness of different loss variants based on different algorithms. Experiments on two real-world datasets show that they perform significantly better than RW-based loss for graph anomaly detection.
Supplemental Material
- Leman Akoglu, Rishi Chandy, and Christos Faloutsos. 2013. Opinion fraud detection in online reviews by network effects. In Seventh international AAAI conference on weblogs and social media.Google Scholar
- Leman Akoglu, Mary McGlohon, and Christos Faloutsos. 2010. Oddball: Spotting anomalies in weighted graphs. In Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer, 410--421.Google ScholarDigital Library
- Leman Akoglu, Hanghang Tong, and Danai Koutra. 2015. Graph based anomaly detection and description: a survey. Data mining and knowledge discovery, Vol. 29, 3 (2015), 626--688.Google ScholarDigital Library
- Reid Andersen. 2010. A local algorithm for finding dense subgraphs. ACM Transactions on Algorithms (TALG), Vol. 6, 4 (2010), 60.Google Scholar
- Yuichi Asahiro, Kazuo Iwama, Hisao Tamaki, and Takeshi Tokuyama. 2000. Greedily finding a dense subgraph. Journal of Algorithms, Vol. 34, 2 (2000), 203--221.Google ScholarDigital Library
- Sambaran Bandyopadhyay, Saley Vishal Vivek, and MN Murty. 2020. Outlier Resistant Unsupervised Deep Architectures for Attributed Network Embedding. In Proceedings of the 13th International Conference on Web Search and Data Mining. 25--33.Google ScholarDigital Library
- Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. 2019. Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss. arXiv preprint arXiv:1906.07413 (2019).Google Scholar
- Deepayan Chakrabarti. 2004. Autopart: Parameter-free graph partitioning and outlier detection. In European Conference on Principles of Data Mining and Knowledge Discovery. Springer, 112--124.Google ScholarCross Ref
- Nitesh V Chawla. 2003. C4. 5 and imbalanced data sets: investigating the effect of sampling method, probabilistic estimate, and decision tree structure. In Proceedings of the ICML, Vol. 3. 66.Google Scholar
- Nitesh V Chawla, Kevin W Bowyer, Lawrence O Hall, and W Philip Kegelmeyer. 2002. SMOTE: synthetic minority over-sampling technique. Journal of artificial intelligence research, Vol. 16 (2002), 321--357.Google ScholarCross Ref
- Kaize Ding, Jundong Li, Rohit Bhanushali, and Huan Liu. 2019 a. Deep anomaly detection on attributed networks. In Proceedings of the 2019 SIAM International Conference on Data Mining. SIAM, 594--602.Google ScholarCross Ref
- Kaize Ding, Yichuan Li, Jundong Li, Chenghao Liu, and Huan Liu. 2019 b. Graph Neural Networks with High-order Feature Interactions. arXiv preprint arXiv:1908.07110 (2019).Google Scholar
- Dhivya Eswaran, Christos Faloutsos, Sudipto Guha, and Nina Mishra. 2018. Spotlight: Detecting anomalies in streaming graphs. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. ACM, 1378--1386.Google ScholarDigital Library
- Jing Gao, Feng Liang, Wei Fan, Chi Wang, Yizhou Sun, and Jiawei Han. 2010. On community outliers and their efficient detection in information networks. In Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 813--822.Google ScholarDigital Library
- Ming Gao, Leihui Chen, Xiangnan He, and Aoying Zhou. 2018. BiNE: Bipartite Network Embedding. In SIGIR. 715--724.Google Scholar
- Aditya Grover and Jure Leskovec. 2016. node2vec: Scalable feature learning for networks. In Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 855--864.Google ScholarDigital Library
- Will Hamilton, Zhitao Ying, and Jure Leskovec. 2017. Inductive representation learning on large graphs. In Advances in Neural Information Processing Systems. 1024--1034.Google Scholar
- Ville Hautamaki, Ismo Karkkainen, and Pasi Franti. 2004. Outlier detection using k-nearest neighbour graph. In Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., Vol. 3. IEEE, 430--433.Google ScholarCross Ref
- Haibo He, Yang Bai, Edwardo A Garcia, and Shutao Li. 2008. ADASYN: Adaptive synthetic sampling approach for imbalanced learning. In 2008 IEEE international joint conference on neural networks (IEEE world congress on computational intelligence). IEEE, 1322--1328.Google Scholar
- Haibo He and Edwardo A Garcia. 2009. Learning from imbalanced data. IEEE Transactions on knowledge and data engineering, Vol. 21, 9 (2009), 1263--1284.Google ScholarDigital Library
- Bryan Hooi, Neil Shah, Alex Beutel, Stephan Günnemann, Leman Akoglu, Mohit Kumar, Disha Makhija, and Christos Faloutsos. 2016a. Birdnest: Bayesian inference for ratings-fraud detection. In Proceedings of the 2016 SIAM International Conference on Data Mining. SIAM, 495--503.Google ScholarCross Ref
- Bryan Hooi, Hyun Ah Song, Alex Beutel, Neil Shah, Kijung Shin, and Christos Faloutsos. 2016b. Fraudar: Bounding graph fraud in the face of camouflage. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 895--904.Google ScholarDigital Library
- Meng Jiang. 2016. Catching Social Media Advertisers with Strategy Analysis. In Proceedings of the First International Workshop on Computational Methods for CyberSafety. ACM, 5--10.Google ScholarDigital Library
- Meng Jiang, Alex Beutel, Peng Cui, Bryan Hooi, Shiqiang Yang, and Christos Faloutsos. 2016a. Spotting suspicious behaviors in multimodal data: A general metric and algorithms. IEEE Transactions on Knowledge and Data Engineering, Vol. 28, 8 (2016), 2187--2200.Google ScholarDigital Library
- Meng Jiang, Peng Cui, Alex Beutel, Christos Faloutsos, and Shiqiang Yang. 2014. Catchsync: catching synchronized behavior in large directed graphs. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 941--950.Google ScholarDigital Library
- Meng Jiang, Peng Cui, Alex Beutel, Christos Faloutsos, and Shiqiang Yang. 2016b. Inferring lockstep behavior from connectivity pattern in large graphs. Knowledge and Information Systems, Vol. 48, 2 (2016), 399--428.Google ScholarDigital Library
- Parisa Kaghazgaran, James Caverlee, and Anna Squicciarini. 2018. Combating crowdsourced review manipulators: A neighborhood-based approach. In Proceedings of the 11th International Conference on Web Search and Data Mining. 306--314.Google ScholarDigital Library
- Sham M Kakade, Karthik Sridharan, and Ambuj Tewari. 2009. On the complexity of linear prediction: Risk bounds, margin bounds, and regularization. In Advances in neural information processing systems. 793--800.Google Scholar
- Thomas N Kipf and Max Welling. 2016a. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016).Google Scholar
- Thomas N Kipf and Max Welling. 2016b. Variational graph auto-encoders. arXiv preprint arXiv:1611.07308 (2016).Google Scholar
- Vladimir Koltchinskii, Dmitry Panchenko, et al. 2002. Empirical margin distributions and bounding the generalization error of combined classifiers. The Annals of Statistics, Vol. 30, 1 (2002), 1--50.Google ScholarCross Ref
- Srijan Kumar, Bryan Hooi, Disha Makhija, Mohit Kumar, Christos Faloutsos, and VS Subrahmanian. 2018. Rev2: Fraudulent user prediction in rating platforms. In Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining. ACM, 333--341.Google ScholarDigital Library
- Srijan Kumar, Francesca Spezzano, VS Subrahmanian, and Christos Faloutsos. 2016. Edge weight prediction in weighted signed networks. In Data Mining (ICDM), 2016 IEEE 16th International Conference on. IEEE, 221--230.Google ScholarCross Ref
- David Mease, Abraham J Wyner, and Andreas Buja. 2007. Boosted classification trees and class probability/quantile estimation. Journal of Machine Learning Research, Vol. 8, Mar (2007), 409--439.Google ScholarDigital Library
- Mathias Niepert, Mohamed Ahmed, and Konstantin Kutzkov. 2016. Learning convolutional neural networks for graphs. In International conference on machine learning. 2014--2023.Google ScholarDigital Library
- Guansong Pang, Longbing Cao, Ling Chen, and Huan Liu. 2018. Learning representations of ultrahigh-dimensional data for random distance-based outlier detection. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 2041--2050.Google ScholarDigital Library
- Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. 2014. Deepwalk: Online learning of social representations. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 701--710.Google ScholarDigital Library
- B Aditya Prakash, Ashwin Sridharan, Mukund Seshadri, Sridhar Machiraju, and Christos Faloutsos. 2010. Eigenspokes: Surprising patterns and scalable community chipping in large graphs. In Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer, 435--448.Google ScholarDigital Library
- Shebuti Rayana and Leman Akoglu. 2015. Collective opinion spam detection: Bridging review networks and metadata. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 985--994.Google ScholarDigital Library
- Neil Shah. 2017. FLOCK: Combating astroturfing on livestreaming platforms. In Proceedings of the 26th International Conference on World Wide Web. International World Wide Web Conferences Steering Committee, 1083--1091.Google ScholarDigital Library
- Neil Shah, Alex Beutel, Brian Gallagher, and Christos Faloutsos. 2014. Spotting suspicious link behavior with fbox: An adversarial perspective. In 2014 IEEE International Conference on Data Mining. IEEE, 959--964.Google ScholarDigital Library
- Kijung Shin, Bryan Hooi, and Christos Faloutsos. 2016. M-zoom: Fast dense-block detection in tensors with quality guarantees. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, 264--280.Google ScholarDigital Library
- Jimeng Sun, Huiming Qu, Deepayan Chakrabarti, and Christos Faloutsos. 2005. Neighborhood formation and anomaly detection in bipartite graphs. In Fifth IEEE International Conference on Data Mining (ICDM'05). IEEE, 8--pp.Google ScholarDigital Library
- Jian Tang, Meng Qu, Mingzhe Wang, Ming Zhang, Jun Yan, and Qiaozhu Mei. 2015. Line: Large-scale information network embedding. In Proceedings of the 24th international conference on world wide web. International World Wide Web Conferences Steering Committee, 1067--1077.Google ScholarDigital Library
- Petar Velivc ković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. 2017. Graph attention networks. arXiv preprint arXiv:1710.10903 (2017).Google Scholar
- Daheng Wang, Meng Jiang, Munira Syed, Oliver Conway, Vishal Juneja, Sriram Subramanian, and Nitesh V Chawla. 2020. Calendar Graph Neural Networks for Modeling Time Structures in Spatiotemporal User Behaviors. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining.Google ScholarDigital Library
- Haibo Wang, Chuan Zhou, Jia Wu, Weizhen Dang, Xingquan Zhu, and Jilong Wang. 2018. Deep structure learning for fraud detection. In 2018 IEEE International Conference on Data Mining (ICDM). IEEE, 567--576.Google ScholarCross Ref
- Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. 2018. How Powerful are Graph Neural Networks? arXiv preprint arXiv:1810.00826 (2018).Google Scholar
- Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William L Hamilton, and Jure Leskovec. 2018. Graph convolutional neural networks for web-scale recommender systems. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. ACM, 974--983.Google ScholarDigital Library
- Wenhao Yu, Mengxia Yu, Tong Zhao, and Meng Jiang. 2020. Identifying referential intention with heterogeneous contexts. In Proceedings of The Web Conference 2020. 962--972.Google ScholarDigital Library
- Chuxu Zhang, Dongjin Song, Chao Huang, Ananthram Swami, and Nitesh V Chawla. 2019. Heterogeneous graph neural network. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 793--803.Google ScholarDigital Library
- Tong Zhao, Yozen Liu, Leonardo Neves, Oliver Woodford, Meng Jiang, and Neil Shah. 2020. Data Augmentation for Graph Neural Networks. arXiv preprint arXiv:2006.06830 (2020).Google Scholar
- Tong Zhao, Matthew Malir, and Meng Jiang. 2018. Actionable objective optimization for suspicious behavior detection on large bipartite graphs. In 2018 IEEE International Conference on Big Data (Big Data). IEEE, 1248--1257.Google ScholarCross Ref
Index Terms
- Error-Bounded Graph Anomaly Loss for GNNs
Recommendations
One-class graph neural networks for anomaly detection in attributed networks
AbstractNowadays, graph-structured data are increasingly used to model complex systems. Meanwhile, detecting anomalies from graph has become a vital research problem of pressing societal concerns. Anomaly detection is an unsupervised learning task of ...
Anomaly detection method of packet loss node location in heterogeneous hash networks
AbstractWhen the current method is used to detect the location anomaly of packet loss nodes in heterogeneous hash networks, the detection takes a long time, and the detection results obtained have large errors, which have the problems of low ...
GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction
WSDM '24: Proceedings of the 17th ACM International Conference on Web Search and Data MiningGraph Anomaly Detection (GAD) is a technique used to identify abnormal nodes within graphs, finding applications in network security, fraud detection, social media spam detection, and various other domains. A common method for GAD is Graph Auto-Encoders (...
Comments