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

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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.
Keywords
Novelty detection, Point processes, Extreme value theory, One-class classification, Process monitoring

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Please use this url to cite or link to this publication:

Chicago
Luca, Stijn, Marco AF Pimentel, Peter J Watkinson, and David A Clifton. 2018. “Point Process Models for Novelty Detection on Spatial Point Patterns and Their Extremes.” Computational Statistics & Data Analysis 125: 86–103.
APA
Luca, S., Pimentel, M. A., Watkinson, P. J., & Clifton, D. A. (2018). Point process models for novelty detection on spatial point patterns and their extremes. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 125, 86–103.
Vancouver
1.
Luca S, Pimentel MA, Watkinson PJ, Clifton DA. Point process models for novelty detection on spatial point patterns and their extremes. COMPUTATIONAL STATISTICS & DATA ANALYSIS. 2018;125:86–103.
MLA
Luca, Stijn et al. “Point Process Models for Novelty Detection on Spatial Point Patterns and Their Extremes.” COMPUTATIONAL STATISTICS & DATA ANALYSIS 125 (2018): 86–103. Print.
@article{8577587,
  abstract     = {Novelty detection is a particular example of pattern recognition identifying patterns that departure from some model of {\textacutedbl}normal behaviour{\textacutedbl}. 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.},
  author       = {Luca, Stijn and Pimentel, Marco AF and Watkinson, Peter J and Clifton, David A},
  issn         = {0167-9473},
  journal      = {COMPUTATIONAL STATISTICS \& DATA ANALYSIS},
  language     = {eng},
  pages        = {86--103},
  title        = {Point process models for novelty detection on spatial point patterns and their extremes},
  url          = {http://dx.doi.org/10.1016/j.csda.2018.03.019},
  volume       = {125},
  year         = {2018},
}

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