Abstract
Dynamic networks are widely used in the social, physical, and biological sciences as a concise mathematical representation of the evolving interactions in dynamic complex systems. Measuring distances between network snapshots is important for analyzing and understanding evolution processes of dynamic systems. To the best of our knowledge, however, existing network distance measures are designed for static networks. Therefore, when measuring the distance between any two snapshots in dynamic networks, valuable context structure information existing in other snapshots is ignored. To guide the construction of context-aware distance measures, we propose a context-aware distance paradigm, which introduces context information to enrich the connotation of the general definition of network distance measures. A Context-aware Spectral Distance (CSD) is then given as an instance of the paradigm by constructing a context-aware spectral representation to replace the core component of traditional Spectral Distance (SD). In a node-aligned dynamic network, the context effectively helps CSD gain mainly advantages over SD as follows: (1) CSD is not affected by isospectral problems; (2) CSD satisfies all the requirements of a metric, while SD cannot; and (3) CSD is computationally efficient. In order to process large-scale networks, we develop a kCSD that computes top-k eigenvalues to further reduce the computational complexity of CSD. Although kCSD is a pseudo-metric, it retains most of the advantages of CSD. Experimental results in two practical applications, i.e., event detection and network clustering in dynamic networks, show that our context-aware spectral distance performs better than traditional spectral distance in terms of accuracy, stability, and computational efficiency. In addition, context-aware spectral distance outperforms other baseline methods.
- Bijaya Adhikari, Yao Zhang, Sorour E Amiri, Aditya Bharadwaj, and B. Aditya Prakash. 2018. Propagation-based temporal network summarization. IEEE Transactions on Knowledge and Data Engineering (TKDE) 30, 4 (2018), 729–742.Google Scholar
Cross Ref
- Nesreen Ahmed, Ryan Anthony Rossi, John Lee, Theodore Willke, Rong Zhou, Xiangnan Kong, and Hoda Eldardiry. 2020. Role-based graph embeddings. IEEE Transactions on Knowledge and Data Engineering (TKDE). 1–1.Google Scholar
Cross Ref
- Nesreen K. Ahmed, Ryan Rossi, John Boaz Lee, Theodore L. Willke, Rong Zhou, Xiangnan Kong, and Hoda Eldardiry. 2018. Learning role-based graph embeddings. arXiv preprint arXiv:1802.02896 (2018).Google Scholar
- Leman Akoglu and Christos Faloutsos. 2013. Anomaly, event, and fraud detection in large network datasets. In Proceedings of the 6th ACM International Conference on Web Search and Data Mining (WSDM’13). 773–774. Google Scholar
Digital Library
- Leman Akoglu, Hanghang Tong, and Danai Koutra. 2015. Graph based anomaly detection and description: A survey. Data Mining and Knowledge Discovery 29, 3 (2015), 626–688. Google Scholar
Digital Library
- Siddharth Bhatia, Bryan Hooi, Minji Yoon, Kijung Shin, and Christos Faloutsos. 2020. Midas: Microcluster-based detector of anomalies in edge streams.. In The 34th AAAI Conference on Artificial Intelligence (AAAI’20). Association for the Advancement of Artificial Intelligence 3242–3249.Google Scholar
- Stefano Boccaletti, Ginestra Bianconi, Regino Criado, Charo I. Del Genio, Jesús Gómez-Gardenes, Miguel Romance, Irene Sendina-Nadal, Zhen Wang, and Massimiliano Zanin. 2014. The structure and dynamics of multilayer networks. Physics Reports 544, 1 (2014), 1–122.Google Scholar
Cross Ref
- Stefano Boccaletti, Vito Latora, Yamir Moreno, Martin Chavez, and D-U. Hwang. 2006. Complex networks: Structure and dynamics. Physics Reports 424, 4–5 (2006), 175–308.Google Scholar
Cross Ref
- Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng, and Jörg Sander. 2000. LOF: Identifying density-based local outliers. In Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data. 93–104. Google Scholar
Digital Library
- Horst Bunke, Peter J. Dickinson, Miro Kraetzl, and Walter D. Wallis. 2007. A Graph-theoretic Approach to Enterprise Network Dynamics. Vol. 24. Springer Science & Business Media.Google Scholar
- Steve Butler and Jason Grout. 2010. A construction of cospectral graphs for the normalized Laplacian. arXiv preprint arXiv:1008.3646 (2010).Google Scholar
- Steve Butler and Kristin Heysse. 2016. A cospectral family of graphs for the normalized Laplacian found by toggling. Linear Algebra Applications 507 (2016), 499–512.Google Scholar
Cross Ref
- Shaosheng Cao, Wei Lu, and Qiongkai Xu. 2015. Grarep: Learning graph representations with global structural information. In Proceedings of the 24th ACM International Conference on Information and Knowledge Management. 891–900. Google Scholar
Digital Library
- Chen Chen and Hanghang Tong. 2015. Fast eigen-functions tracking on dynamic graphs. In Proceedings of the 2015 SIAM International Conference on Data Mining. SIAM, 559–567.Google Scholar
Cross Ref
- Fan R. K. Chung and Fan Chung Graham. 1997. Spectral Graph Theory. Number 92. American Mathematical Society.Google Scholar
- Manlio De Domenico and Jacob Biamonte. 2016. Spectral entropies as information-theoretic tools for complex network comparison. Physical Review X 6, 4 (2016), 041062.Google Scholar
- Manlio De Domenico, Vincenzo Nicosia, Alexandre Arenas, and Vito Latora. 2015. Structural reducibility of multilayer networks. Nature Communications 6 (2015), 6864.Google Scholar
Cross Ref
- Yuxiao Dong, Nitesh V. Chawla, and Ananthram Swami. 2017. metapath2vec: Scalable representation learning for heterogeneous networks. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’17). 135–144. Google Scholar
Digital Library
- Claire Donnat, Susan Holmes, et al. 2018. Tracking network dynamics: A survey using graph distances. Annals of Applied Statistics 12, 2 (2018), 971–1012.Google Scholar
Cross Ref
- Claire Donnat, Marinka Zitnik, David Hallac, and Jure Leskovec. 2018. Learning structural node embeddings via diffusion wavelets. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD’18). ACM, 1320–1329. Google Scholar
Digital Library
- Daniel M. Dunlavy, Tamara G. Kolda, and Evrim Acar. 2011. Temporal link prediction using matrix and tensor factorizations. ACM Transactions on Knowledge Discovery From Data 5, 2 (2011), 10. Google Scholar
Digital Library
- Joseph C. Dunn. 1974. Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics 4, 1 (1974), 95–104.Google Scholar
Cross Ref
- Daniele Durante, Nabanita Mukherjee, and Rebecca C. Steorts. 2017. Bayesian learning of dynamic multilayer networks. Journal of Machine Learning Research 18, 43 (2017), 1–29. Google Scholar
Digital Library
- 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 (KDD’18). 1378–1386. Google Scholar
Digital Library
- Damien Fay, Hamed Haddadi, Andrew W. Moore, Richard Mortier, Steve Uhlig, and Almerima Jamakovic. 2010. A weighted spectrum metric for comparison of internet topologies. ACM SIGMETRICS Performance Evaluation Review 37, 3 (2010), 67–72. Google Scholar
Digital Library
- Timothy La Fond, Jennifer Neville, and Brian Gallagher. 2018. Designing size consistent statistics for accurate anomaly detection in dynamic networks. ACM Transactions on Knowledge Discovery from Data (TKDD) 12, 4 (2018), 46. Google Scholar
Digital Library
- Edward B. Fowlkes and Colin L. Mallows. 1983. A method for comparing two hierarchical clusterings. Journal of the American Statistical Association 78, 383 (1983), 553–569.Google Scholar
Cross Ref
- Xinbo Gao, Bing Xiao, Dacheng Tao, and Xuelong Li. 2010. A survey of graph edit distance. Pattern Analysis and Applications 13, 1 (2010), 113–129.Google Scholar
Digital Library
- Gene H. Golub and Charles F. Van Loan. 2012. Matrix Computations. Vol. 3. JHU Press.Google Scholar
- Jiao Gu, Jürgen Jost, Shiping Liu, and Peter F. Stadler. 2016. Spectral classes of regular, random, and empirical graphs. Linear Algebra and its Applications 489 (2016), 30–49.Google Scholar
- Petter Holme and Jari Saramäki. 2012. Temporal networks. Physics Reports 519, 3 (2012), 97–125.Google Scholar
Cross Ref
- Yuriy Hulovatyy, Huili Chen, and Tijana Milenkovic. 2015. Exploring the structure and function of temporal networks with dynamic graphlets. Bioinformatics 31, 12 (2015), 2402–2402.Google Scholar
Cross Ref
- Giuseppe Jurman, Roberto Visintainer, and Cesare Furlanello. 2011. An introduction to spectral distances in networks. In Proceedings of the 2011 Conference on Neural Nets WIRN10: Proceedings of the 20th Italian Workshop on Neural Nets. 227–234. Google Scholar
Digital Library
- Danai Koutra, Neil Shah, Joshua T. Vogelstein, Brian Gallagher, and Christos Faloutsos. 2016. DeltaCon: Principled massive-graph similarity function with attribution. ACM Transactions on Knowledge Discovery from Data (TKDD) 10, 3 (2016), 28. Google Scholar
Digital Library
- Richard B. Lehoucq and Danny C. Sorensen. 1996. Deflation techniques for an implicitly restarted Arnoldi iteration. SIAM Journal on Matrix Analysis and Applications 17, 4 (1996), 789–821. Google Scholar
Digital Library
- Jure Leskovec, Lada A. Adamic, and Bernardo A. Huberman. 2007. The dynamics of viral marketing. ACM Transactions on the Web (TWEB) 1, 1 (2007), 5. Google Scholar
Digital Library
- Michael Levandowsky and David Winter. 1971. Distance between sets. Nature 234, 5323 (1971), 34.Google Scholar
- Jundong Li, Harsh Dani, Xia Hu, Jiliang Tang, Yi Chang, and Huan Liu. 2017. Attributed network embedding for learning in a dynamic environment. In Proceedings of the 2017 ACM on Conference on Information and Knowledge Management. ACM, 387–396. Google Scholar
Digital Library
- Richard Lippmann, Robert K. Cunningham, David J. Fried, Isaac Graf, Kris R. Kendall, Seth E. Webster, and Marc A. Zissman. 1999. Results of the DARPA 1998 Offline Intrusion Detection Evaluation.. In Recent Advances in Intrusion Detection, Vol. 99. 829–835. Google Scholar
Digital Library
- Yike Liu, Tara Safavi, Abhilash Dighe, and Danai Koutra. 2018. Graph summarization methods and applications: A survey. ACM Computing Surveys (CSUR) 51, 3 (2018), 62. Google Scholar
Digital Library
- Linyuan Lü, Liming Pan, Tao Zhou, Yi-Cheng Zhang, and H. Eugene Stanley. 2015. Toward link predictability of complex networks. Proceedings of the National Academy of Sciences 112, 8 (2015), 2325–2330.Google Scholar
Cross Ref
- Guixiang Ma, Chun Ta Lu, Lifang He, Philip S. Yu, and Ann B. Ragin. 2017. Multi-view graph embedding with hub detection for brain network analysis. In 2017 IEEE International Conference on Data Mining (ICDM’17). 967–972.Google Scholar
- Naoki Masuda and Petter Holme. 2019. Detecting sequences of system states in temporal networks. Scientific Reports 9, 1 (2019), 795.Google Scholar
Cross Ref
- Nathan D. Monnig and François G. Meyer. 2018. The resistance perturbation distance: A metric for the analysis of dynamic networks. Discrete Applied Mathematics 236 (2018), 347–386. Google Scholar
Digital Library
- Mingdong Ou, Peng Cui, Jian Pei, Ziwei Zhang, and Wenwu Zhu. 2016. Asymmetric transitivity preserving graph embedding. In Proceedings of the 22th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD’16). 1105–1114. Google Scholar
Digital Library
- Panagiotis Papadimitriou, Ali Dasdan, and Hector Garcia-Molina. 2008. Web graph similarity for anomaly detection (poster). In Proceedings of the 17th International Conference on World Wide Web (WWW’08). ACM, 1167–1168. Google Scholar
Digital 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 & Data Mining (KDD’14). 701–710. Google Scholar
Digital Library
- Brandon Pincombe. 2005. Anomaly detection in time series of graphs using ARMA processes. ASOR Bulletin 24, 4 (2005), 2.Google Scholar
- Brandon Pincombe. 2007. Detecting changes in time series of network graphs using minimum mean squared error and cumulative summation. ANZIAM Journal 48 (2007), 450–473.Google Scholar
Cross Ref
- Jiezhong Qiu, Yuxiao Dong, Hao Ma, Jian Li, Kuansan Wang, and Jie Tang. 2018. Network embedding as matrix factorization: Unifying deepwalk, line, pte, and node2vec. In Proceedings of the 11th ACM International Conference on Web Search and Data Mining (WSDM’18). 459–467. Google Scholar
Digital Library
- Shebuti Rayana and Leman Akoglu. 2016. Less is more: Building selective anomaly ensembles. ACM Transactions on Knowledge Discovery from Data (TKDD) 10, 4 (2016), 42. Google Scholar
Digital Library
- Manuel Gomez Rodriguez, Jure Leskovec, and Bernhard Schölkopf. 2013. Structure and dynamics of information pathways in online media. In Proceedings of the 6th ACM International Conference on Web Search and Data Mining (WSDM’13). 23–32. Google Scholar
Digital Library
- Sudeep Sarkar and Kim L. Boyer. 1998. Quantitative measures of change based on feature organization: Eigenvalues and eigenvectors. Computer vision and Image Understanding 71, 1 (1998), 110–136. Google Scholar
Digital Library
- Arlei Silva, Ambuj Singh, and Ananthram Swami. 2018. Spectral algorithms for temporal graph cuts. In Proceedings of the 27th International Conference on World Wide Web (WWW’18). ACM, 519–528. Google Scholar
Digital Library
- Juliette Stehlé, Nicolas Voirin, Alain Barrat, Ciro Cattuto, Lorenzo Isella, Jean-François Pinton, Marco Quaggiotto, Wouter Van den Broeck, Corinne Régis, Bruno Lina, et al. 2011. High-resolution measurements of face-to-face contact patterns in a primary school. PloS One 6, 8 (2011), e23176.Google Scholar
Cross Ref
- Gilbert W. Stewart. 1990. Matrix perturbation theory. (1990).Google Scholar
- Alexander Strehl and Joydeep Ghosh. 2002. Cluster ensembles—A knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research 3(Dec.2002), 583–617. Google Scholar
Digital Library
- Jie Tang. 2017. Computational models for social network analysis: A brief survey. In Proceedings of the 26th International Conference on World Wide Web (WWW’17) Companion. ACM, 921–925. Google Scholar
Digital Library
- Jian Tang, Meng Qu, and Qiaozhu Mei. 2015. Pte: Predictive text embedding through large-scale heterogeneous text networks. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’15). 1165–1174. Google Scholar
Digital 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 (WWW’15). 1067–1077. Google Scholar
Digital Library
- Cunchao Tu, Han Liu, Zhiyuan Liu, and Maosong Sun. 2017. CANE: Context-aware network embedding for relation modeling. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), Vol. 1. 1722–1731.Google Scholar
Cross Ref
- Richard C. Wilson and Ping Zhu. 2008. A study of graph spectra for comparing graphs and trees. Pattern Recognition 41, 9 (2008), 2833–2841. Google Scholar
Digital Library
- Haowen Xu, Wenxiao Chen, Nengwen Zhao, Zeyan Li, Jiahao Bu, Zhihan Li, Ying Liu, Youjian Zhao, Dan Pei, Yang Feng, et al. 2018. Unsupervised anomaly detection via variational auto-encoder for seasonal KPIs in web applications. In Proceedings of the 27th International Conference on World Wide Web (WWW’18). ACM, 187–196. Google Scholar
Digital Library
- Minji Yoon, Bryan Hooi, Kijung Shin, and Christos Faloutsos. 2019. Fast and accurate anomaly detection in dynamic graphs with a two-pronged approach. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD’19). 647–657. Google Scholar
Digital Library
- Jie Zhou, Ganqu Cui, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, and Maosong Sun. 2018. Graph neural networks: A review of methods and applications.arXiv preprint arXiv:1812.08434 (2018).Google Scholar
- Dingyuan Zhu, Peng Cui, Ziwei Zhang, Jian Pei, and Wenwu Zhu. 2018. High-order proximity preserved embedding for dynamic networks. IEEE Transactions on Knowledge and Data Engineering (TKDE) 30, 11 (2018), 2134–2144.Google Scholar
Digital Library
Index Terms
Context-aware Distance Measures for Dynamic Networks
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