Detecting statistically significant geographical anomalous regions from spatial sampling points by coupling Gaussian function and multidirectional optimization

Abstract

An anomalous geographical region refers to a collection of spatially aggregated objects whose non‐spatial attribute values are significantly inconsistent with those of their spatial neighbors. The detection of anomalous regions plays an important role in spatial data mining. However, the requirement of user‐specified parameters for spatial neighborhood construction and anomalous region discovery will inevitably result in the omission or misjudgment of spatial anomalies; it is still challenging to detect arbitrarily shaped anomalous regions in an objective way. Inspired by the data field theory, this study models spatial anomaly degree by considering the distance decay effect and develops an approach for the objective detection of significantly anomalous regions from spatial sampling points. First, constrained Delaunay triangulation is employed to construct reasonable and stable spatial neighborhoods by quantifying the spatial distribution characteristics of sampling points. On this basis, a Gaussian function is adopted for the measurement of spatial anomaly degree considering both distance decay effect and non‐spatial attribute value differences, based upon which anomalous objects can be captured. Finally, treating each anomalous object as a seed, a multidirectional optimization method is developed to identify arbitrarily shaped anomalous regions, and a Monte Carlo simulation is employed to further test the statistical significance of anomalous regions. Experiments on both simulated and real‐world datasets demonstrate that the proposed approach outperforms existing methods in terms of both accuracy and sufficiency for anomalous region detection.