Spatio‐temporal classification in point patterns under the presence of clutter

Abstract

We consider the problem of detection of features in the presence of clutter for spatio‐temporal point patterns. In previous studies, related to the spatial context, Kth nearest‐neighbor distances to classify points between clutter and features. In particular, a mixture of distributions whose parameters were estimated using an expectation‐maximization algorithm. This paper extends this methodology to the spatio‐temporal context by considering the properties of the spatio‐temporal Kth nearest‐neighbor distances. For this purpose, we make use of a couple of spatio‐temporal distances, which are based on the Euclidean and the maximum norms. We show close forms for the probability distributions of such Kth nearest‐neighbor distances and present an intensive simulation study together with an application to earthquakes.