A non‐parametric statistical test method to detect significant cross‐outliers in spatial points

Abstract

In spatial points that describe geographical events, outliers that deviate significantly from the global or local distribution indicate extraordinary geographical phenomena.Existing outlier detection methods cannot statistically identify significant outliers by considering the co-occurrences of multiple categories of spatial points. Therefore, this study develops a non-parametric statistical test method to detect significant cross-outliers from two categories of spatial points divided into primary and reference ones. Firstly, the cross K function is employed to test the significance of co-occurrences of the two categories of points, and the cooccurrence intensity of each primary point is quantitatively defined as the number of reference points in its circular buffer. Then, the edge-constrained Delaunay triangulation is utilized to construct a reasonable spatial neighborhood for each primary point. On this basis, the Monte Carlo method is utilized to simulate the distribution of reference points in the support domain of each primary point delineated using the α-shape algorithm, and those primary points with significantly different local co-occurrence intensity are determined as spatial cross-outliers. Finally, those crossoutliers obtained using different buffers are evaluated further by analysis of living intervals. Experiments on both simulated and real-life datasets demonstrate the effectiveness and practicability of the proposed method.

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

“…For gridded or polygon datasets, the spatial neighborhoods can be determined directly based on the topological relationships between spatial objects (Han, Kamber, & Pei, 2012). For spatial sampling points, there are some widely used spatial neighborhood construction methods, such as eps ‐neighborhood (Han et al., 2012; Liu, Tang, Deng, & Shi, 2015), k‐ nearest neighborhood (Chawla & Sun, 2006; Chen, Lu, Kou, & Chen, 2008; Lu et al., 2011), graph‐based neighborhood using Voronoi diagram (Qu, 2008) or Delaunay triangulation (Deng et al., 2018; Shi et al., 2017; Shi, Gong, et al., 2018). The parameters eps and k are required to be assigned when constructing the eps ‐neighborhood and k‐ nearest neighborhood, respectively.…”

“…However, it is unavoidable that the generated graphs lack accuracy in boundary and hole regions, which will further have negative effects on the calculation of spatial anomaly degree. To handle this problem, the constrained Delaunay triangulation has been developed to eliminate those inconsistent long edges to obtain more reliable spatial neighborhoods (Deng et al., 2018). However, spatial neighborhoods constructed by direct connections through edges of constrained Delaunay triangulation still lack insufficiency when a spatial‐point dataset has various local densities.…”

“… Adaptive spatial neighborhood construction. The constrained Delaunay triangulation, which has been proven to be an effective tool to express spatial proximity relationships among objects (Deng, Liu, Cheng, & Shi, 2011; Deng et al, 2018; Shi et al., 2017), is employed to construct adaptive spatial neighborhoods. Robust spatial outlier degree measurement. Spatial anomaly degree quantifies the local deviation of spatial objects in terms of non‐spatial attribute values.…”

“…For spatial anomaly detection, the most critical issue is the expression of spatial proximity relationships (Ernst & Haesbroeck, 2017; Janeja, Adam, Atluri, & Vaidya, 2010). Related studies have demonstrated the effectiveness and power of Delaunay triangulation in capturing spatial proximity relationships (Deng et al., 2011, 2018; Shi et al., 2017). In initial Delaunay triangulation, there may exist many significantly long edges in areas with sparse points, such as those edges intersected with dashed lines in Figure 2a.…”

“…This type of significant deviation is potentially generated by a special mechanism instead of just useless noise (Hawkins, 1980). In this case, the detection of spatial anomalies can make positive contributions to reveal the potential occurrence mechanism of significant changes and surprising patterns in geographic phenomena (Chandola, Banerjee, & Kumar, 2009; de Smith, Goodchild, & Longley, 2018; Miller & Han, 2009; Shekhar, Li, Ali, Eftelioglu, & Jiang, 2017), such as abnormal distribution of epidemic disease and crime (Deng et al., 2018; Janeja & Palanisamy, 2013; Shi, Gong, Deng, Yang, & Xu, 2018), extreme climate events (Shi, Deng, Yang, & Liu, 2016; Telang, Deepak, Joshi, & Deshpande, & Rajendran, 2014), and urban traffic congestion (Shi, Deng, Yang, & Gong, 2018; Shi & Janeja, 2011).…”