基于引力模型的空间自相关分析集成框架
An Integrated Framework of Spatial Autocorrelation Analysis Based on Gravity Model
AI总结：
本文通过数学推导将引力模型与空间自相关分析整合为统一框架，推导出势能测度、相关方程及Moran's index等统计量，并以城市系统数据验证其应用价值。
摘要：
空间交互与空间自相关是地理空间分析的两个不同领域，揭示二者之间的内在联系将有助于发展地理分析的理论与方法。本文致力于通过数学推导从引力模型演绎出一套空间相关分析模型。主要结果如下。第一，从引力模型推导出一组势能测度。第二，基于势能公式的二次型构造了一对相关方程，包括内积方程和外积方程。第三，从势能公式推导出一系列空间自相关统计量，包括Moran's index和Getis-Ord's index。第四，将分形维数概念引入空间权重矩阵。采用城市系统的观测数据进行实证分析，展示了新推导模型的应用流程。可以得出结论：空间自相关实际上根植于空间交互过程，通过将空间自相关模型与引力模型整合到同一框架中，可以发展出一种改进的空间分析方法论。
英文摘要：
Spatial interaction and spatial autocorrelation are two different fields of geo-spatial analysis, revealing the internal relationship between the two fields will help to develop the theory and method of geographical analysis. This paper is devoted to deducing a system of spatial correlation analysis models from the gravity model by mathematical derivation. The main results are as follows. First, a set of potential energy measurements are derived from the gravity model. Second, a pair of correlation equations, including an inner product equation and an outer product equation, are constructed based on the quadratic form of potential energy formula. Third, a series of spatial autocorrelation statistics, including Moran's index and Getis-Ord's index are derived from the potential energy formula. Fourth, the concept of fractal dimension is introduced into spatial weight matrix. The observational data of urban systems are employed to make an empirical analysis, demonstrating the application procedure of newly derived models. A conclusion can be drawn that spatial autocorrelation is actually rooted in spatial interaction process, and an improved methodology of spatial analysis can be developed by integrating spatial autocorrelation models and gravity model into the same framework.
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