Revisiting Attribute Independence Assumption in Probabilistic Unsupervised Anomaly Detection

  • Sunil AryalEmail author
  • Kai Ming Ting
  • Gholamreza Haffari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9650)


In this paper, we revisit the simple probabilistic approach of unsupervised anomaly detection by estimating multivariate probability as a product of univariate probabilities, assuming attributes are generated independently. We show that this simple traditional approach performs competitively to or better than five state-of-the-art unsupervised anomaly detection methods across a wide range of data sets from categorical, numeric or mixed domains. It is arguably the fastest anomaly detector. It is one order of magnitude faster than the fastest state-of-the-art method in high dimensional data sets.


Fast anomaly detection Independence assumption Big data 



We would like to thank Prof. Takashi Washio for providing very useful comments and suggestions. We are thankful to the anonymous reviewers for their critical comments to improve the quality of the paper.


  1. 1.
    Chandola, V., Banerjee, A., Kumar, V.: Anomaly detection: a survey. ACM Comput. Surv. 41(3), 15: 1–15: 58 (2009)CrossRefGoogle Scholar
  2. 2.
    Ramaswamy, S., Rastogi, R., Shim, K.: Efficient algorithms for mining outliers from large data sets. In: Proceedings of the 2000 ACM SIGMOD Conference on Management of Data, pp. 427–438 (2000)Google Scholar
  3. 3.
    Breunig, M.M., Kriegel, H.P., Ng, R.T., Sander, J.: LOF: identifying density-based local outliers. In: Proceedings of ACM SIGMOD Conference on Management of Data, pp. 93–104 (2000)Google Scholar
  4. 4.
    Liu, F., Ting, K.M., Zhou, Z.H.: Isolation forest. In: Proceedings of the Eighth IEEE International Conference on Data Mining, (ICDM), pp. 413–422 (2008)Google Scholar
  5. 5.
    Sugiyama, M., Borgwardt, K.M.: Rapid distance-based outlier detection via sampling. In: Proceedings of the 27th Annual Conference on Neural Information Processing Systems, Lake Tahoe, Nevada, United States, pp. 467–475 (2013)Google Scholar
  6. 6.
    He, Z., Xu, X., Huang, J.Z., Deng, S.: FP-outlier: frequent pattern based outlier detection. Comput. Sci. Inf. Syst. 2(1), 103–118 (2005)CrossRefGoogle Scholar
  7. 7.
    Akoglu, L., Tong, H., Vreeken, J., Faloutsos, C.: Fast and reliable anomaly detection in categorical data. In: Proceedings of the 21st ACM Conference on Information and Knowledge Management (CIKM), pp. 415–424 (2012)Google Scholar
  8. 8.
    Goldstein, M., Dengel, A.: Histogram-based outlier score (hbos): a fast unsupervised anomaly detection algorithm. In: Proceedings of the 35th German Conference on Artificial Intelligence (KI-2012), pp. 59–63 (2012)Google Scholar
  9. 9.
    Chandola, V., Boriah, S., Kumar, V.: Similarity measures for categorical data: a comparative study. Technical report TR 07–022, Department of Computer Science and Engineering, University of Minnesota, USA (2007)Google Scholar
  10. 10.
    Agrawal, R., Imieliński, T., Swami, A.: Mining association rules between sets of items in large databases. In: Proceedings of the 1993 ACM SIGMOD Conference on Management of Data, pp. 207–216 (1993)Google Scholar
  11. 11.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley-Interscience, New York (2000)zbMATHGoogle Scholar
  12. 12.
    Bache, K., Lichman, M.: UCI machine learning repository, University of California, Irvine, School of Information and Computer Sciences (2013).
  13. 13.
    Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The weka data mining software: an update. SIGKDD Explor. Newslett. 11(1), 10–18 (2009)CrossRefGoogle Scholar
  14. 14.
    Bay, S.D., Schwabacher, M.: Mining distance-based outliers in near linear time with randomization and a simple pruning rule. In: Proceedings of the Ninth ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 29–38 (2003)Google Scholar
  15. 15.
    Beygelzimer, A., Kakade, S., Langford, J.: Cover trees for nearest neighbor. In: Proceedings of the 23rd International Conference on Machine Learning, pp. 97–104 (2006)Google Scholar
  16. 16.
    Keller, F., Mller, E., Bhm, K.: HiCS: high contrast subspaces for density-based outlier ranking. In: Proceedings of ICDE, pp. 1037–1048. IEEE Computer Society (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Sunil Aryal
    • 1
    • 2
    Email author
  • Kai Ming Ting
    • 2
  • Gholamreza Haffari
    • 1
  1. 1.Clayton School of Information TechnologyMonash UniversityVictoriaAustralia
  2. 2.School of Engineering and Information TechnologyFederation UniversityVictoriaAustralia

Personalised recommendations