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Point process models for novelty detection on spatial point patterns and their extremes

Author

Listed:
  • Luca, Stijn E.
  • Pimentel, Marco A.F.
  • Watkinson, Peter J.
  • Clifton, David A.

Abstract

Novelty detection is a particular example of pattern recognition identifying patterns that departure from some model of “normal behaviour”. The classification of point patterns is considered that are defined as sets of N observations of a multivariate random variable X and where the value N follows a discrete stochastic distribution. The use of point process models is introduced that allow us to describe the length N as well as the geometrical configuration in data space of such patterns. It is shown that such infinite dimensional study can be translated into a one-dimensional study that is analytically tractable for a multivariate Gaussian distribution. Moreover, for other multivariate distributions, an analytic approximation is obtained, by the use of extreme value theory, to model point patterns that occur in low-density regions as defined by X. The proposed models are demonstrated on synthetic and real-world data sets.

Suggested Citation

  • Luca, Stijn E. & Pimentel, Marco A.F. & Watkinson, Peter J. & Clifton, David A., 2018. "Point process models for novelty detection on spatial point patterns and their extremes," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 86-103.
    • Handle: RePEc:eee:csdana:v:125:y:2018:i:c:p:86-103
    DOI: 10.1016/j.csda.2018.03.019
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