Skip to main content

Computational Preliminaries

  • Chapter
  • First Online:
Outlier Detection: Techniques and Applications

Abstract

This chapter presents the mathematical notation followed to represent the data and the computational measures defined on the data. Basics of matrix algebra and information theory are furnished as they form the building blocks of the computational model followed here. The standard procedure for preparing data sets of various types to perform outlier detection is also covered. In essence, the objective is to present the computational preliminaries necessary for developing various algorithmic methods for outlier detection in multi-dimensional record data as well as anomaly detection in network/graph data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aggarwal, C.C., Yu, P.S.: Outlier detection for high dimensional data. In: ACM SIGMOD International Conference on Management of Data, pp. 37–46. Santa Barbara, USA (2001)

    Article  Google Scholar 

  2. Bock, H.H.: The classical data situation. In: Analysis of Symbolic Data, pp. 139–152. Springer (2002)

    Google Scholar 

  3. Boriah, S., Chandola, V., Kumar, V.: Similarity measures for categorical data: a comparative evaluation. In: SIAM International Conference on Data Mining, Atlanta, Georgia, USA, pp. 243–254 (2008)

    Google Scholar 

  4. Chandola, V., Banerjee, A., Kumar, V.: Anomaly detection: a survey. ACM Comput. Surv. 41(3) (2009)

    Article  Google Scholar 

  5. Chandola, V., Boriah, S., Kumar, V.: A framework for exploring categorical data. In: SDM, pp. 187–198. SIAM (2009)

    Chapter  Google Scholar 

  6. Chaudhary, A., Szalay, A.S., Szalay, E.S., Moore, A.W.: Very fast outlier detection in large multidimensional data sets. In: ACM SIGMOD Workshop in Research Issues in Data Mining and Knowledge Discovery, pp. 45–52 (2002)

    Google Scholar 

  7. Cheng, V., Li, C.H., Kwok, J., Li, C.K.: Dissimilarity learning for nominal data. Patten Recognit. 37(7), 1471–1477 (2004)

    Article  Google Scholar 

  8. Davis, J., Goadrich, M.: The relationship between precision-recall and ROC curves. In: 23rd International Conference on Machine Learning (ICML), pp. 30–38 (2006)

    Google Scholar 

  9. Emmott, A.F., Das, S., Deitterich, T., Fern, A., Wong, W.K.: Systematic construction of anomaly detection benchmarks from real data. In: KDD Workshop on Outlier Detection and Description. ACM, Chicago, IL, USA (2013)

    Google Scholar 

  10. Fawcett, T.: An introduction to ROC analysis. Pattern Recognit. Lett. 27, 861–874 (2006)

    Article  Google Scholar 

  11. Gower, J.C., Legendre, P.: Metric and euclidean properties of dissimilarity coefficients. J. Classif. 3(1), 5–48 (1986)

    Article  MathSciNet  Google Scholar 

  12. Harkins, S., He, H., Williams, G.J., Baxter, R.A.: Outlier detection using replicator neural networks. In: Kambayashi, Y., Winiwarter, W., Arikawa, M. (eds.) 4th International Conference on Data Warehousing and Knowledge Discovery (DaWak). LNCS, vol. 2454, pp. 170–180. Springer, Aixen-Provence, France (2002)

    Google Scholar 

  13. Hido, S., Tsuboi, Y., Kashima, H., Sugiyama, M., Kanamori, T.: Statistical outlier detection using direct density ratio estimation. Knowl. Inf. Syst. 26(2), 309–336 (2011)

    Article  Google Scholar 

  14. Jain, A.K., Duin, R.P.W., Mao, J.: Statistical pattern recognition: a review. IEEE Trans. Pattern Anal Mach. Intell. 22, 4–37 (2000)

    Article  Google Scholar 

  15. Lazarevic, A., Ertoz, L., Kumar, V., Ozgur, A., Srivastava, J.: A comparative study of anomaly detection schemes in network intrusion detection. In: SIAM International Conference on Data Mining (2003)

    Google Scholar 

  16. Leskovec, J., Krevl, A.: SNAP datasets: stanford large network dataset collection (2014). http://snap.stanford.edu/data

  17. Ng, M.K., Li, M.J., Huang, J.Z., He, Z.: On the impact of dissimilarity measure in k-modes clustering algorithm. IEEE Trans. Pattern Anal. Mach. Intell. 29(3), 503–507 (2007)

    Article  Google Scholar 

  18. Sithirasenan, E., Muthukkumarasamy, V.: Substantiating security threats using group outlier detection techniques. In: IEEE GLOBECOM, pp. 2179–2184 (2008)

    Google Scholar 

  19. Stanfill, C., Waltz, D.: Towards memory-based reasoning. Commun. ACM 29(12), 1213–1228 (1986)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. N. R. Ranga Suri .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ranga Suri, N.N.R., Murty M, N., Athithan, G. (2019). Computational Preliminaries. In: Outlier Detection: Techniques and Applications. Intelligent Systems Reference Library, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-030-05127-3_4

Download citation

Publish with us

Policies and ethics