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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. [ABSTRACT FROM AUTHOR]

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 co‐occurrence 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 cross‐outliers 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. [ABSTRACT FROM AUTHOR]

Abstract: The clustering of spatio‐temporal events has become one of the most important research branches of spatio‐temporal data mining. However, the discovery of clusters of spatio‐temporal events with different shapes and densities remains a challenging problem because of the subjectivity in the choice of two critical parameters: the spatio‐temporal window for estimating the density around each event, and the density threshold for evaluating the significance of clusters. To make the clustering of spatio‐temporal events objective, in this study these two parameters were adaptively generated from statistical information about the dataset. More precisely, the density threshold was statistically modeled as an adjusted significance level controlled by the cardinality and support domain of the dataset, and the appropriate sizes of spatio‐temporal windows for clustering were determined by the spatio‐temporal classification entropy and stability analysis. Experiments on both simulated and earthquake datasets were conducted, and the results show that the proposed method can identify clusters of different shapes and densities. [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]