One-class classification of point patterns of extremes

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 = {X-1 ,..., X-k} subset of 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

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

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

Anomaly detection using the Poisson process limit for extremes

Anomaly detection starts from a model of normal behavior and classifies departures from this model as anomalies. This paper introduces a statistical non-parametric approach for anomaly detection that is based on a multivariate extension of the Poisson point process model for univariate extremes. The method is demonstrated on both a synthetic and a real-world data set, the latter being an unbalanced data set of acceleration data collected from movements of 7 pediatric patients suffering from epilepsy that is previously studied in [1]. The positive predictive values could be improved with an increase up to 12.9% (and a mean of 7%) while the sensitivity scores stayed unaltered. The proposed method was also shown to outperform an one-class SVM classifier. Because the Poisson point process model of extremes is able to combine information on the number of excesses over a fixed threshold with that on the excess values, a powerful model to detect anomalies is obtained that can be of high value in many application