一种空间权重矩阵的优化方法

在地理学空间自相关的分析中，权重矩阵对整个分析结果有着较大影响。常见的权重矩阵，例如车矩阵、皇后矩阵、距离权重矩阵和k-邻近矩阵，都有各自的优势和缺点。提出了一种基于长度面积比例的空间权重矩阵（ratio of length and area，RLA），并以近年来危害最大的几种传染病之一——病毒性肝炎在中国大陆各省份的发病率为例进行了实验分析。实验结果表明，RLA矩阵能够很好地实现空间权重矩阵的基本功能，是常见的车矩阵的一种更为广义的定义，并且可以更加自由地实现空间自相关的分析。利用本空间权重矩阵能够更好地模拟不同地理单元之间的邻接关系，为流行病的预防提供支持。

An Improved Spatial Weights Matrix Construction Strategy

In the study of geographical spatial autocorrelation, the spatial weights matrix is regarded as a fundamental and essential field area of research. In this paper, we firstly analyze the advantages and disadvantages of several common weights matrixes like ROOK matrix, QUEEN matrix and K-Nearest matrix. Considering the improvements for in the traditional spatial weights matrix, we put forward RLA (Ratio of Length and Area) which isthat can be applied with a stricter measurement standards and representsing the relative relationship of a spatial unit to other adjacent ones units instead of a simple true or false discrimination to improve the accuracy. For verification, we carry carried out experiments on the Mainland China viral hepatitis statistical data from 2004 to 2012 of Mainland China based on the provincial administrative divisions. The rResults indicate that the proposed weights matrix not only achieves the fundamental functions of a spatial weights matrix, but also is treated as a general definition of ROOK matrix, freely applicable to when implementing spatial autocorrelation analysis. The adoption of this RLA spatial weights matrix will further reveal the spatial relationships among different geographical units, also providing support for the prevention of epidemics.