Detecting Clustering Scales with the Incremental K-Function: Comparison Tests on Actual and Simulated Geospatial Datasets

The detection of so-called hot-spots in point datasets is important to generalize the spatial structures and properties in geospatial datasets. This is all the more important when spatial big data analytics is concerned. The K-function is regarded as one of the most effective methods to detect departures from randomness, high concentrations of point events and to examine the scale properties of a spatial point pattern. However, when applied to a pattern exhibiting local clusters, it can hardly determine the true scales of an observed pattern. We use a variant of the K-function that examines the number of events within a particular distance increment rather than the total number of events within a distance range. We compare the Incremental K-function to the standard K-function in terms of its fundamental properties and demonstrate the differences using several simulated point processes, which allow us to explore the range of conditions under which differences are obtained, as well as on a real-world geospatial dataset.