## One-class classification of point patterns of extremes

*Stijn Luca, David A. Clifton, Bart Vanrumste*; 17(191):1−21, 2016.

### Abstract

Novelty detection or one-class classification starts from a
model describing some type of `normal behaviour' and aims to
classify deviations from this model as being either novelties or
anomalies. In this paper the problem of novelty detection for
point patterns $S=\{\mathbf{x}_1,\ldots ,\mathbf{x}_k\}\subset
\mathbb{R}^d$ is treated where examples of anomalies are very sparse, or
even absent. The latter complicates the tuning of
hyperparameters in models commonly used for novelty detection,
such as one-class support vector machines and hidden Markov
models. To this end, the use of extreme value statistics is
introduced to estimate explicitly a model for the abnormal class
by means of extrapolation from a statistical model $X$ for the
normal class. We show how multiple types of information obtained
from any available extreme instances of $S$ can be combined to
reduce the high false-alarm rate that is typically encountered
when classes are strongly imbalanced, as often occurs in the
one-class setting (whereby `abnormal' data are often scarce).
The approach is illustrated using simulated data and then a
real-life application is used as an exemplar, whereby
accelerometry data from epileptic seizures are analysed - these
are known to be extreme and rare with respect to normal
accelerometer data.

[abs][pdf][bib]