Feature detection in point processes on linear networks using nearest neighbour volumes

TL;DR

This paper introduces a novel method for feature detection in point processes on linear networks using K-th nearest neighbor volumes, effectively distinguishing features from clutter in complex geometric settings.

Contribution

It extends existing classification methods to linear networks, enabling analysis of superimposed Poisson processes for feature detection in cluttered environments.

Findings

Method successfully distinguishes features from clutter in simulations.

Applied to real-world traffic accident data in Colombia.

Demonstrates effectiveness in complex linear network contexts.

Abstract

We consider the feature detection problem in the presence of clutter in point processes on linear networks. 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. We use the K-th nearest neighbour volumes distribution in linear networks for this approach. As a result, our method is suitable for analysing point patterns consisting of features and clutter as two superimposed Poisson processes 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.