Clustering in point processes on linear networks using nearest neighbour volumes

This study introduces a novel method specifically designed to detect clusters of points within linear networks. This method extends a classification approach used for point processes in spatial contexts. Unlike traditional methods that operate on planar spaces, our approach adapts to the unique geometric challenges of linear networks, where classical properties of point processes are altered, and intuitive data visualisation becomes more complex. Our method utilises the distribution of the <i>K</i>th nearest neighbour volumes, extending planar-based clustering techniques to identify regions of increased point density within a network. This approach is particularly effective for distinguishing overlapping Poisson processes within the same linear network. We demonstrate the practical utility of our method through applications to road traffic accident data from two Colombian cities, Bogota and Medellin. Our results reveal distinct clusters of high-density points in road segments where severe traffic accidents (resulting in injuries or fatalities) are most likely to occur, highlighting areas of increased risk. These clusters were primarily located on major arterial roads with high traffic volumes. In contrast, low-density points corresponded to areas with fewer accidents, likely due to lower traffic flow or other mitigating factors. Our findings provide valuable insights for urban planning and road safety management.