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.

中文翻译：

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结合高斯函数和多向优化从空间采样点检测统计显着地理异常区域

异常地理区域是指空间聚合对象的集合，其非空间属性值与其空间邻居的非空间属性值显着不一致。异常区域的检测在空间数据挖掘中起着重要的作用。然而，空间邻域构建和异常区域发现对用户指定参数的要求，不可避免地会导致空间异常的遗漏或误判；客观地检测任意形状的异常区域仍然具有挑战性。本研究受数据场理论的启发，通过考虑距离衰减效应对空间异常程度进行建模，并开发了一种从空间采样点客观检测显着异常区域的方法。第一的，采用约束德劳内三角剖分法，通过量化采样点的空间分布特征，构建合理稳定的空间邻域。在此基础上，考虑距离衰减效应和非空间属性值差异，采用高斯函数测量空间异常程度，以此为基础对异常物体进行捕获。最后，将每个异常对象视为种子，开发了一种多方向优化方法来识别任意形状的异常区域，并采用蒙特卡罗模拟进一步检验异常区域的统计显着性。