One-Class Classification of Point Patterns of Extremes

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.