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

We consider the problem of detection of features in the presence of clutter for spatio-temporal point patterns. This problem was previously treated but only in the spatial context. In particular, Byers et al. (1998) used k-th nearest neighbour distances to classify points between clutter and features. They proposed a mixture of distributions whose parameters were estimated using an EM algorithm. This paper extends this methodology to the spatio-temporal context by considering the properties of the spatio-temporal k-th nearest neighbour distances. We make use of several spatio-temporal n- dimensional distances (n − 1 spatial dimensions, and 1 temporal dimension), that are mixtures of defined distances for the p-norm. We show close forms for the probability distributions of such k- th nearest neighbour distances. We also present an intensive simulation study that covers a wide range of practical scenarios.