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

Stijn E. Luca, Marco A.F. Pimentel, Peter J. Watkinson and David A. Clifton

Computational Statistics & Data Analysis, 2018, vol. 125, issue C, 86-103

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 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:125:y:2018:i:c:p:86-103

DOI: 10.1016/j.csda.2018.03.019

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