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The discovery of spatial clusters formed by proximal spatial units with similar non-spatial attribute values plays an important role in spatial data analysis. Although several spatial contiguity-constrained clustering methods are currently available, almost all of them discover clusters in a geographical dataset, even though the dataset has no natural clustering structure. Statistically evaluating the significance of the degree of homogeneity within a single spatial cluster is difficult. To overcome this limitation, this study develops a permutation test approach Specifically, the homogeneity of a spatial cluster is measured based on the local variance and cluster member permutation, and two-stage permutation tests are developed to determine the significance of the degree of homogeneity within each spatial cluster. The proposed permutation tests can be integrated into the existing spatial clustering algorithms to detect homogeneous spatial clusters. The proposed tests are compared with four existing tests (i.e., Park's test, the contiguity-constrained nonparametric analysis of variance (COCOPAN) method, spatial scan statistic, and q-statistic) using two simulated and two meteorological datasets. The comparison shows that the proposed two-stage permutation tests are more effective to identify homogeneous spatial clusters and to determine homogeneous clustering structures in practical applications. [ABSTRACT FROM AUTHOR]

Spatial co-location pattern mining aims to discover a collection of Boolean spatial features, which are frequently located in close geographic proximity to each other. Existing methods for identifying spatial co-location patterns usually require users to specify two thresholds, i.e. the prevalence threshold for measuring the prevalence of candidate co-location patterns and distance threshold to search the spatial co-location patterns. However, these two thresholds are difficult to determine in practice, and improper thresholds may lead to the misidentification of useful patterns and the incorrect reporting of meaningless patterns. The multi-scale approach proposed in this study overcomes this limitation. Initially, the prevalence of candidate co-location patterns is measured statistically by using a significance test, and a non-parametric model is developed to construct the null distribution of features with the consideration of spatial auto-correlation. Next, the spatial co-location patterns are explored at multi-scales instead of single scale (or distance threshold) discovery. The validity of the co-location patterns is evaluated based on the concept of lifetime. Experiments on both synthetic and ecological datasets show that spatial co-location patterns are discovered correctly and completely by using the proposed method; on the other hand, the subjectivity in discovery of spatial co-location patterns is reduced significantly. [ABSTRACT FROM AUTHOR]

A fundamental element of exploratory spatial data analysis is the discovery of clusters in a spatial point dataset. When clusters with distinctly different local densities exist, the determination of suitable density level is still an unsolved problem. On that account, an iterative detection and removal method is proposed in this study. In each step of the novel method, there are two stages. In the detection stage, density level is statistically modeled as a significance level controlled by the number and support domain of the points in the dataset, and then a hypothesis test is used to detect the high-density points. In the removal stage, the Delaunay triangulation network is used to construct clusters and support domains for the identified high-density points, and then the high-density points and their support domains are removed from the dataset. The detection and removal operation are iteratively implemented until no high-density points can be detected. Experiments and comparisons show that the proposed method, on the one hand, outperforms four state-of-the-art methods for detecting clusters of complex shapes and diverse densities, and on the other hand, no user-specified parameters are required. In addition, the support domains of clusters are very useful for spatial analysis. [ABSTRACT FROM AUTHOR]

Spatial point data is an important data source that represents the locations of spatial events (such as crime, disease cases, and earthquakes). Detecting clusters I n spatial point data plays a key role in exploratory spatial data analysis. Although much attention has been paid to the clustering of spatial points, how to automatically and efficiently discover the statistically significant clusters with irregular shapes is still a challenging work. On that account, an automatic method to detect the statistically significant high-density clusters in spatial point data with noise is proposed in this paper. First, the Voronoi diagram of the spatial points is constructed, and the densities of spatial points are defined by the areas of the Voronoi cells. Then, high-density points are automatically detected using spatial hotspot statistics analysis, and a density-based clustering strategy is further adapted to combine the neighboring high-density points into candidate clusters. Finally, a statistical significance test is proposed to evaluate the significance of the candidate clusters under the spatially homogeneous or heterogeneous distribution assumption. We tested the proposed method with the simulated data sets and the real-world taxi trajectory data for detecting the pick-up hotspot regions in Wuhan, China. Results show that the proposed method can successfully find arbitrarily shaped significant clusters that existing state-of-the-art clustering algorithms may fail to find in spatial point data with noise. • A method to detect statistically significant spatial point clusters is proposed. • Spatial cold spot statistics are applied to detect spatial point clusters. • Statistic constrained clustering method is proposed to detect candidate clusters. • Monte-Carlo permutation test is applied to evaluate the significance of clusters. • The proposed method has good performances and great potential in cluster detection. [ABSTRACT FROM AUTHOR]

It has been established that spatial clustering patterns are scale-dependent. However, scale is still not explicitly handled in existing methods to detect clusters in spatial points; thus, users are often puzzled by the varied clustering results obtained by different spatial clustering methods and/or parameters. To handle the effect of scale on the cluster detection of spatial points, two kinds of scales are first specified in this study: scale of data and scale of analysis. These two kinds of scales are embodied by a set of three indictors: data resolution, spatial extent, and analysis resolution. Further, a scale-driven clustering model with these three scale indicators as parameters is statistically constructed based on the Natural Principle and graph theory. A comparative study of this scale-driven clustering model with existing methods is carried out with a simulated spatial dataset. It is found that only this new method is able to discover the multi-scale spatial clustering patterns defined in the benchmarks. Further, Carex lasiocarpa population data is used to illustrate the practical value of the proposed scale-driven clustering model. [ABSTRACT FROM AUTHOR]