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Novelty Detection with Multivariate Extreme Value Statistics

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Abstract

Novelty detection, or one-class classification, aims to determine if data are “normal” with respect to some model of normality constructed using examples of normal system behaviour. If that model is composed of generative probability distributions, the extent of “normality” in the data space can be described using Extreme Value Theory (EVT), a branch of statistics concerned with describing the tails of distributions. This paper demonstrates that existing approaches to the use of EVT for novelty detection are appropriate only for univariate, unimodal problems. We generalise the use of EVT for novelty detection to the analysis of data with multivariate, multimodal distributions, allowing a principled approach to the analysis of high-dimensional data to be taken. Examples are provided using vital-sign data obtained from a large clinical study of patients in a high-dependency hospital ward.

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Notes

  1. independent and identically distributed

  2. Note that this probabilistic approach contrasts with another popular method of novelty detection, that of one-class support vector machines (SVMs) [21].

  3. alternatively known as mixing coefficients or weights

  4. Noting that the superscript ‘+’ refers to the distribution of maxima.

  5. Noting that this is an asymptotic relationship, which is true as the number of data m→ ∞.

  6. termed the reduced variate

  7. The EVD \(f_n^e\) is implicitly parameterised by the number of observations in the dataset, m. Thus, each value of m will yield a different EVD \(f_n^e\).

  8. and radially symmetric

  9. and where there is no global symmetry

  10. This is a component-wise extremum, as described earlier.

References

  1. Bishop, C. M. (1995). Neural networks for pattern recognition. Oxford: Oxford University Press.

    Google Scholar 

  2. Bishop, C. M. (2006). Pattern recognition and machine learning. Berlin: Springer.

    MATH  Google Scholar 

  3. Castillo, E., Hadi, A. S., Balakrishnan, N., & Sarabia, J. M. (2005). Extreme value and related models with applications in engineering and science. New York: Wiley.

    MATH  Google Scholar 

  4. Clifton, D. (2009). Novelty detection with extreme value theory in jet engine vibration data. Ph.D. thesis, University of Oxford.

  5. Clifton, D., McGrogan, N., Tarassenko, L., King, S., Anuzis, P., & King, D. (2008). Bayesian extreme value statistics for novelty detection in gas-turbine engines. In Proceedings of IEEE aerospace (pp. 1–11). Montana, USA.

  6. Clifton, D., Tarassenko, L., Sage, C., & Sundaram, S. (2008). Condition monitoring of manufacturing processes. In Proceedings of condition monitoring 2008 (pp. 273–279). Edinburgh, UK.

  7. Coles, S. (2001). An introduction to statistical modeling of extreme values. Berlin: Springer-Verlag.

    MATH  Google Scholar 

  8. Embrechts, P., Kluppelberg, C., & Mikosch, T. (2008). Modelling extremal events for insurance and finance (4th Ed.). Berlin: Springer.

    Google Scholar 

  9. Fisher, R. A., & Tippett, L. H. C. (1928). Limiting forms of the frequency distributions of the largest or smallest members of a sample. Proceedings of the Cambridge Philosophical Society, 24, 180–190.

    Article  MATH  Google Scholar 

  10. Hann, A. (2008). Multi-parameter monitoring for early warning of patient deterioration. Ph.D. thesis, University of Oxford.

  11. Hayton, P., Tarassenko, L., Schölkopf, B., & Anuzis, P. (2000). Support vector novelty detection applied to jet engine vibration spectra. In Proceedings of NIPS (pp. 946–952). London.

  12. Hravnak, M., Edwards, L., Clontz, A., Valenta, C., DeVita, M., & Pinsky, M. (2008). Defining the incidence of cardiorespiratory instability in patients in step-down units using an electronic integrated monitoring system. Archives of Internal Medicine, 168(12), 1300–1308.

    Article  Google Scholar 

  13. Hravnak, M., Edwards, L., Clontz, A., Valenta, C., DeVita, M., & Pinsky, M. (2008). Impact of electronic integrated monitoring system upon the incidence and duration of patient instability on a step down unit. In Proceedings of 4th international medical emergency team conference. Toronto.

  14. Hyndman, R. (1996). Computing and graphing high density regions. The American Statistician, 50(2), 120–126.

    Article  MathSciNet  Google Scholar 

  15. Ilonen, J., Paalanen, P., Kamarainen, J., & Kälviäinen, H. (2006). Gaussian mixture PDF in one-class classification: Computing and using confidence values. In Proceedings of the 18th international conference on pattern recognition (pp. 577–580).

  16. Lauer, M. (2001). A mixture approach to novelty detection using training data with outliers. In Proceedings of the 12th European conference on machine learning, ECML. Lecture notes in computer science (Vol. 2167, pp. 300–311).

  17. Nairac, A., Corbett-Clark, T., Ripley, R., Townsend, N., & Tarassenko, L. (1997). Choosing an appropriate model for novelty detection. In Proceeding of the 5th IEE international conference on artificial neural networks (pp. 227–232). Cambridge.

  18. Paalanen, P., Kamarainen, J., Ilonen, J., & Kälviäinen (2006). Feature representation and discrimination based on Gaussian mixture model probability densities—practices and algorithms. Pattern Recognition, 39, 1346–1358.

    Article  MATH  Google Scholar 

  19. Roberts, S. J. (1999). Novelty detection using extreme value statistics. IEE Proceedings on Vision, Image and Signal Processing, 146(3), 124–129.

    Article  Google Scholar 

  20. Roberts, S. J. (2000). Extreme value statistics for novelty detection in biomedical signal processing. IEE Proceedings on Science, Technology and Measurement, 47(6), 363–367.

    Article  Google Scholar 

  21. Schölkopf, B., Williamson, R., Smola, A. J., Shawe-Taylor, J., & Platt, J. (1999). Support vector method for novelty detection. In Proceedings of NIPS (pp. 582–588).

  22. Scott, D. (1992). Multivariate density estimation. Theory, practice and visualization. New York: Wiley.

    Book  MATH  Google Scholar 

  23. Sohn, H., Allen, D. W., Worden, K., & Farrar, C. (2005). Structural damage classification using extreme value statistics. Journal of Dynamic Systems, Measurement, and Control, 127(1), 125–132.

    Article  Google Scholar 

  24. Tarassenko, L., Hann, A., Patterson, A., Braithwaite, E., Davidson, K., Barber, V., et al. (2005). Biosign: Multi-parameter monitoring for early warning of patient deterioration. In Proceedings of the 3rd IEEE international seminar on medical applications of signal processing (pp. 71–76).

  25. Tarassenko, L., Hann, A., & Young, D. (2006). Integrated monitoring and analysis for early warning of patient deterioration. British Journal of Anaesthesia, 98(1), 149–152.

    Google Scholar 

  26. Tarassenko, L., Hayton, P., Cerneaz, N., & Brady, M. (1995). Novelty detection for the identification of masses in mammograms. In Proceedings of the 4th IEE international conference on artificial neural networks (Vol. 4, pp. 442–447). Perth, Australia.

  27. Tarassenko, L., Nairac, A., Townsend, N., Buxton, I., & Cowley, P. (2000). Novelty detection for the identification of abnormalities. International Journal of Systems Science, 31(11), 1427–1439.

    Article  MATH  Google Scholar 

  28. Worden, K., Manson, G., & Allman, D. (2003). Experimental validation of a structural health monitoring methodology: Part I. Novelty detection on a laboratory structure. Journal of Sound and Vision, 259(2), 323–343.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Old Road Campus, Roosevelt Drive, Oxford, OX3 7DQ, UK

    David Andrew Clifton, Samuel Hugueny & Lionel Tarassenko

Authors
  1. David Andrew Clifton
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  2. Samuel Hugueny
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  3. Lionel Tarassenko
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Corresponding author

Correspondence to David Andrew Clifton.

Additional information

This work was supported by the NIHR Biomedical Research Centre, Oxford; the EPSRC LSI Doctoral Training Centre, Oxford; and the Centre of Excellence in Personalised Healthcare funded by the Wellcome Trust and EPSRC under grant number WT 088877/Z/09/Z.

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Clifton, D.A., Hugueny, S. & Tarassenko, L. Novelty Detection with Multivariate Extreme Value Statistics. J Sign Process Syst 65, 371–389 (2011). https://doi.org/10.1007/s11265-010-0513-6

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  • DOI: https://doi.org/10.1007/s11265-010-0513-6

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