Outlier detection with partial information: application to emergency mapping

Abstract

This paper, addresses the problem of novelty detection in the case that the observed data is a mixture of a known ‘background’ process contaminated with an unknown other process, which generates the outliers, or novel observations. The framework we describe here is quite general, employing univariate classification with incomplete information, based on knowledge of the distribution (the probability density function, pdf) of the data generated by the ‘background’ process. The relative proportion of this ‘background’ component (the prior ‘background’ probability), the pdf and the prior probabilities of all other components are all assumed unknown. The main contribution is a new classification scheme that identifies the maximum proportion of observed data following the known ‘background’ distribution. The method exploits the Kolmogorov–Smirnov test to estimate the proportions, and afterwards data are Bayes optimally separated. Results, demonstrated with synthetic data, show that this approach can produce more reliable results than a standard novelty detection scheme. The classification algorithm is then applied to the problem of identifying outliers in the SIC2004 data set, in order to detect the radioactive release simulated in the ‘joker’ data set. We propose this method as a reliable means of novelty detection in the emergency situation which can also be used to identify outliers prior to the application of a more general automatic mapping algorithm.