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We introduce an extreme function theory as a novel method by which probabilistic novelty detection may be performed with functions, where the functions are represented by time-series of (potentially multivariate) discrete observations. We set the method within the framework of Gaussian processes (GP), which offers a convenient means of constructing a distribution over functions. Whereas conventional novelty detection methods aim to identify individually extreme data points, with respect to a model of normality constructed using examples of 'normal' data points, the proposed method aims to identify extreme functions, with respect to a model of normality constructed using examples of 'normal' functions, where those functions are represented by time-series of observations. The method is illustrated using synthetic data, physiological data acquired from a large clinical trial, and a benchmark time-series dataset. © 2007-2012 IEEE.

Original publication

DOI

10.1109/JSTSP.2012.2234081

Type

Journal article

Journal

IEEE Journal on Selected Topics in Signal Processing

Publication Date

04/02/2013

Volume

7

Pages

28 - 37