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 forspatio-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 usingan expectation-maximization algorithm. This paper extends this methodology tothe spatio-temporal context by considering the properties of the spatio-temporalKth nearest-neighbor distances. For this purpose, we make use of a couple ofspatio-temporal distances, which are based on the Euclidean and the maxi-mum norms. We show close forms for the probability distributions of suchKthnearest-neighbor distances and present an intensive simulation study togetherwith an application to earthquakes.