Clustering in Point Processes on Linear Networks Using Nearest Neighbour Volumes

In this study, we address the challenge of detecting clusters within linear networks, focusing on the classification of point processes. We extend the classification method developed in previous studies to this more complex geometric context, where the classical properties of a point process change and data visualization are not intuitive. Our approach leverages the distribution of the K-th nearest neighbour volumes in linear networks. Consequently, our methodology is well-suited for analysing point patterns comprising two overlapping Poisson processes occurring on the same linear network. To illustrate the method, we present simulations and examples of road traffic accidents that resulted in injuries or deaths in two cities in Colombia.