Novelty Detection with Multivariate Extreme Value Statistics

Novelty detection, or one-class classification, aims to determine if data are "normal" with respect to some model of normality constructed using examples of normal system behaviour. If that model is composed of generative probability distributions, the extent of "normality" in the data space can be described using Extreme Value Theory (EVT), a branch of statistics concerned with describing the tails of distributions. This paper demonstrates that existing approaches to the use of EVT for novelty detection are appropriate only for univariate, unimodal problems. We generalise the use of EVT for novelty detection to the analysis of data with multivariate, multimodal distributions, allowing a principled approach to the analysis of high-dimensional data to be taken. Examples are provided using vital-sign data obtained from a large clinical study of patients in a high-dependency hospital ward.