Outlier detection with arbitrary probability functions

Abstract

We consider the problem of unsupervised outlier detection in large collections of data objects when objects are modeled by means of arbitrary multidimensional probability density functions. Specifically, we present a novel definition of outlier in the context of uncertain data under the attribute level uncertainty model, according to which an uncertain object is an object that always exists but its actual value is modeled by a multivariate pdf. The notion of outlier provided is distance-based, in that an uncertain object is declared to be an outlier on the basis of the expected number of its neighbors in the data set. To the best of our knowledge this is the first work that considers the unsupervised outlier detection problem on the full feature space on data objects modeled by means of arbitrarily shaped multidimensional distribution functions. Properties that allow to reduce the number of probability distance computations are presented, together with an efficient algorithm for determining the outliers in an input uncertain data set. © Springer International Publishing Switzerland 2013.