论文标题
基于Moran索引的空间自相关方程
Spatial autocorrelation equation based on Moran's index
论文作者
论文摘要
基于标准化矢量和全球归一化的重量矩阵，Moran的空间自相关分析指数已表示为二次形式的公式。此外，基于此公式，可以为Moran索引构建标准矢量的内部产品方程和外部产品方程。但是，这些方程的理论基础和应用方向尚不清楚。本文致力于探索Moran索引的内部和外部产品方程。这些方法包括数学推导和经验分析。结果如下。首先，基于内部产品方程，可以构建两个空间自相关模型。一个带有恒定的术语，另一个没有恒定的术语。空间自相关模型可以通过回归分析来计算Moran的指数。其次，内部和外部产品方程可用于改善Moran的散点图。与传统的Moran的散点图相比，标准化的Moran的散点图可以显示更多的地理空间信息。可以得出一个结论，空间自相关模型是有用的空间分析工具，可以补充空间自相关系数和空间自动回归模型的用途。这些模型有助于理解Moran索引和空间自回归建模过程的边界值。
Based on standardized vector and globally normalized weight matrix, Moran's index of spatial autocorrelation analysis has been expressed as a formula of quadratic form. Further, based on this formula, an inner product equation and outer product equation of the standardized vector can be constructed for Moran's index. However, the theoretical foundations and application direction of these equations are not yet clear. This paper is devoted to exploring the inner and outer product equations of Moran's index. The methods include mathematical derivation and empirical analysis. The results are as follows. First, based on the inner product equation, two spatial autocorrelation models can be constructed. One bears constant terms, and the other bear no constant term. The spatial autocorrelation models can be employed to calculate Moran's index by regression analysis. Second, the inner and outer product equations can be used to improve Moran's scatterplot. The normalized Moran's scatterplot can show more geospatial information than the conventional Moran's scatterplot. A conclusion can be reached that the spatial autocorrelation models are useful spatial analysis tools, complementing the uses of spatial autocorrelation coefficient and spatial autoregressive models. These models are helpful for understanding the boundary values of Moran's index and spatial autoregressive modeling process.
