Classification of spatio-temporal point pattern in the presence of clutter using K-th nearest neighbour distances

In a point process spatio-temporal framework, we consider the problem of features detection in the presence of clutters. We extend the methodology of Byers and Raftery (1998) to the spatio-temporal context by considering the properties of the K-th nearest-neighbour distances. We make use of the spatio-temporal distance based on the Euclidean norm where the temporal term is properly weighted. We show the form of the probability distributions of such K-th nearest-neighbour distance. A mixture distribution, whose parameters are estimated with an EM algorithm, is used to classify points into clutters or features. We assess the performance of the proposed approach with a simulation study, together with an application to earthquakes.