Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T11:16:51.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistical evaluation of spectral methods for anomaly detection in static networks

Published online by Cambridge University Press:  23 September 2019

Tomilayo Komolafe Open the ORCID record for Tomilayo Komolafe [Opens in a new window] ,
A. Valeria Quevedo Open the ORCID record for A. Valeria Quevedo [Opens in a new window] ,
Srijan Sengupta Open the ORCID record for Srijan Sengupta [Opens in a new window]  and
William H. Woodall
Tomilayo Komolafe*
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: [email protected]; [email protected])
A. Valeria Quevedo
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: [email protected]; [email protected]) Faculty of Engineering, Universidad de Piura, Peru (e-mail: [email protected])
Srijan Sengupta
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: [email protected]; [email protected])
William H. Woodall
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: [email protected]; [email protected])
*
*Corresponding author. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The topic of anomaly detection in networks has attracted a lot of attention in recent years, especially with the rise of connected devices and social networks. Anomaly detection spans a wide range of applications, from detecting terrorist cells in counter-terrorism efforts to identifying unexpected mutations during ribonucleic acid transcription. Fittingly, numerous algorithmic techniques for anomaly detection have been introduced. However, to date, little work has been done to evaluate these algorithms from a statistical perspective. This work is aimed at addressing this gap in the literature by carrying out statistical evaluation of a suite of popular spectral methods for anomaly detection in networks. Our investigation on the statistical properties of these algorithms reveals several important and critical shortcomings that we make methodological improvements to address. Further, we carry out a performance evaluation of these algorithms using simulated networks and extend the methods from binary to count networks.

Keywords

residual matrixspectral methodsR-MAT modelprincipal components
Type
Original Article
Information
Network Science , Volume 7 , Issue 3 , September 2019 , pp. 319 - 352
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aiello, W., Chung, F., & Lu, L. (2001). A random graph model for power law graphs. Experimental Mathematics, 10(1), 53–66.CrossRefGoogle Scholar
Akoglu, L., McGlohon, M., & Faloutsos, C. (2010). Oddball: Spotting anomalies in weighted graphs. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 410–421). Springer, Berlin, Heidelberg.CrossRefGoogle Scholar
Akoglu, L., Tong, H., & Koutra, D. (2015). Graph based anomaly detection and description: a survey. Data Mining and Knowledge Discovery, 29(3), 626–688.CrossRefGoogle Scholar
Albert, R., Albert, I., & Nakarado, G. L. (2004). Structural vulnerability of the North American power grid. Physical Review E, 69(2), 025103.CrossRefGoogle ScholarPubMed
Azarnoush, B., Paynabar, K., Bekki, J., & Runger, G. (2016). Monitoring temporal homogeneity in attributed network streams. Journal of Quality Technology, 48(1), 28–43.CrossRefGoogle Scholar
Bader, D. A., & Madduri, K. (2008). Snap, small-world network analysis and partitioning: An open-source parallel graph framework for the exploration of large-scale networks. In 2008 IEEE international symposium on parallel and distributed processing, 2008, Miami, FL (pp. 1–12). IEEE.Google Scholar
Cer, R., Bruce, K., Donohue, D., Temiz, N., Mudunuri, U., Yi, M., … Stephens, R. (2012). Searching for non-B DNA-forming motifs using nBMST (non-B DNA motif search tool). Current Protocols in Human Genetics (pp. 18.7.1–18.7.22).CrossRefGoogle Scholar
Cer, R. Z., Bruce, K. H., Donohue, D. E., Temiz, A. N., Bacolla, A., Mudunuri, U. S., … Collins, J. R. (2011). Introducing the non-B DNA Motif Search Tool (nBMST). Genome Biology, 12(1), P34.CrossRefGoogle Scholar
Chakrabarti, D., Zhan, Y., & Faloutsos, C. (2004). R-MAT: A recursive model for graph mining. In Proceedings of the 2004 SIAM International Conference on Data Mining, Lake Buena Vista, FL (pp. 442–446). SIAM.CrossRefGoogle Scholar
Chawla, S., & Sun, P. (2006). SLOM: A new measure for local spatial outliers. Knowledge and Information Systems, 9(4), 412–429.CrossRefGoogle Scholar
Chung, F., Lu, L., & Vu, V. (2004). Spectra of random graphs with given expected degrees. Internet Mathematics, 1(3), 257–275.CrossRefGoogle Scholar
Dahan, M., Sela, L., & Amin, S. (2017). Network monitoring under strategic disruptions. arXiv preprint arXiv:1705.00349.Google Scholar
Erdos, P., & Rényi, A. (1960). On the evolution of random graphs. Publication of the Mathematical Institute of the Hungarian Academy of Sciences, 5(1), 17–60.Google Scholar
Farahani, E. M., Kazemzadeh, R. B., Noorossana, R., & Rahimian, G. (2017). A statistical approach to social network monitoring. Communications in Statistics-Theory and Methods, 46(22), 11272–11288.CrossRefGoogle Scholar
Haveliwala, T. H. (2003). Topic-sensitive pagerank: A context-sensitive ranking algorithm for web search. IEEE Transactions on Knowledge and Data Engineering, 15(4), 784–796.CrossRefGoogle Scholar
Lei, J., & Rinaldo, A. (2015). Consistency of spectral clustering in stochastic block models. The Annals of Statistics, 43(1), 215–237.CrossRefGoogle Scholar
Mall, R., Langone, R., & Suykens, J. A. (2013). Kernel spectral clustering for big data networks. Entropy, 15(5), 1567–1586.CrossRefGoogle Scholar
Miller, B. A., Beard, M. S., Wolfe, P. J., & Bliss, N. T. (2015). A spectral framework for anomalous subgraph detection. IEEE Transactions on Signal Processing, 63(16), 4191–4206.CrossRefGoogle Scholar
Miller, B. A., Bliss, N., & Wolfe, P. J. (2010a). Subgraph detection using eigenvector L1 norms. Advances in Neural Information Processing Systems, 23, 1633–1641.Google Scholar
Miller, B. A., Bliss, N. T., & Wolfe, P. J. (2010b). Toward signal processing theory for graphs and non-Euclidean data. In 2010 IEEE Proceedings International Conference on Acoustics, Speech and Signal Processing, Dallas, Texas (pp. 5414–5417). ICASSP.CrossRefGoogle Scholar
Nadarajah, S., & Kotz, S. (2004). The beta Gumbel distribution. Mathematical Problems in Engineering, 4, 323–332.CrossRefGoogle Scholar
Newman, M. (2016). Community detection in networks: Modularity optimization and maximum likelihood are equivalent. arXiv preprint arXiv:1606.02319.Google Scholar
Papadimitriou, S., Kitagawa, H., Gibbons, P. B., & Faloutsos, C. (2003). Loci: Fast outlier detection using the local correlation integral. In Proceedings 19th International Conference on Data Engineering, Bangalore, India pp. 315–326. IEEE.Google Scholar
Priebe, C. E., Conroy, J. M., Marchette, D. J., & Park, Y. (2005). Scan statistics on Enron graphs. Computational & Mathematical Organization Theory, 11(3), 229–247.CrossRefGoogle Scholar
Procter, J. B., Thompson, J., Letunic, I., Creevey, C., Jossinet, F., & Barton, G. J. (2010). Visualization of multiple alignments, phylogenies and gene family evolution. Nature Methods, 7, S16–S25.CrossRefGoogle ScholarPubMed
Qin, T., & Rohe, K. (2013). Regularized spectral clustering under the degree-corrected stochastic blockmodel. In Advances in Neural Information Processing Systems, Lake Tahoe, NV (pp. 3120–3128).Google Scholar
Ranshous, S., Shen, S., Koutra, D., Harenberg, S., Faloutsos, C., & Samatova, N. F. (2015). Anomaly detection in dynamic networks: A survey. Wiley Interdisciplinary Reviews: Computational Statistics, 7(3), 223–247.CrossRefGoogle Scholar
Raulf-Heimsoth, M., Chen, Z., Rihs, H., Kalbacher, H., Liebers, V., & Baur, X. (1998). Analysis of t-cell reactive regions and HLA-DR4 binding motifs on the latex allergen Hev b 1 (rubber elongation factor). Clinical and Experimental Allergy, 28(3), 339–348.CrossRefGoogle Scholar
Rohe, K., Chatterjee, S., & Yu, B. (2011). Spectral clustering and the high-dimensional stochastic blockmodel. The Annals of Statistics, 39(4), 1878–1915.CrossRefGoogle Scholar
Šaltenis, V. (2004). Outlier detection based on the distribution of distances between data points. Informatica, 15(3), 399–410.Google Scholar
Savage, D., Zhang, X., Yu, X., Chou, P., & Wang, Q. (2014). Anomaly detection in online social networks. Social Networks, 39, 62–70.CrossRefGoogle Scholar
Sengupta, S. (2018). Anomaly detection in static networks using egonets. arXiv preprint arXiv:1807.08925.Google Scholar
Sengupta, S., & Chen, Y. (2015). Spectral clustering in heterogeneous networks. Statistica Sinica, 25, 1081–1106.Google Scholar
Singh, N., Miller, B. A., Bliss, N. T., & Wolfe, P. J. (2011). Anomalous subgraph detection via sparse principal component analysis. In 2011 IEEE Statistical Signal Processing Workshop (SSP), Nice, France (pp. 485–488). IEEE.CrossRefGoogle Scholar
Sun, J., Qu, H., Chakrabarti, D., & Faloutsos, C. (2005). Neighborhood formation and anomaly detection in bipartite graphs. In Fifth IEEE International Conference on Data Mining (ICDM’05), Houston, TX (pp. 1–8). IEEE.Google Scholar
Wang, G., Xie, S., Liu, B., & Yu, P. S. (2012). Identify online store review spammers via social review graph. ACM Transactions on Intelligent Systems and Technology (TIST), 3(4), 61.Google Scholar
Woodall, W. H., Zhao, M. J., Paynabar, K., Sparks, R., & Wilson, J. D. (2017). An overview and perspective on social network monitoring. IISE Transactions, 49(3), 354–365.CrossRefGoogle Scholar
Supplementary material: PDF

Komolafe et al. supplementary material

Komolafe et al. supplementary material

Download Komolafe et al. supplementary material(PDF)
PDF 4 MB