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Spatial association between regionalizations using the information-theoretical V-measure

机译：使用信息理论V测度的区域间空间关联

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摘要

There is a keen interest in calculating spatial associations between two variables spanning the same study area. Many methods for calculating such associations have been proposed, but the case when both variables are categorical is underdeveloped despite the fact that many datasets of interest are in the form of either regionalizations or thematic maps. In this paper, we advance this case by adapting the so-called V-measure method from its original information-theoretical formulation to the analysis of variance formulation which provides more insight for spatial analysis. We present a step-by-step derivation of the V-measure from the perspective of the analysis of variance. The method produces three indices of global association and two sets of local association indicators which could be mapped to indicate spatial distribution of association strength. The open-source software for calculating all indices from vector datasets accompanies the paper. To showcase the utility of the V-measure, we identified three different application contexts: comparative, associative, and derivative, and present an example of each of them. The V-measure method has several advantages over the widely used Mapcurves method, it has clear interpretations in terms of mutual information as well as in terms of analysis of variance, it provides more precise assessment of association, it is ready-to-use through the accompanying software, and the examples given in the paper serves as a guide to the gamut of its possible applications. Two specific contributions stemming from our re-analysis of the V-measure are the finding of the conceptual flaw in the Geographical Detector-a method to quantify associations between numerical and categorical spatial variables, and a proposal for the new, cartographically based algorithm for finding an optimal number of regions in clustering-derived regionalizations.
机译：人们对计算跨越同一研究区域的两个变量之间的空间关联非常感兴趣。已经提出了许多用于计算这种关联的方法，但是尽管许多感兴趣的数据集都以区域化或专题图的形式出现，但两个变量都是分类的情况仍未得到开发。在本文中，我们通过将所谓的V测度方法从其原始的信息理论公式化为方差分析公式，从而为空间分析提供了更多的见识，来改进这种情况。我们从方差分析的角度介绍了V度量的逐步推导。该方法产生三个全局关联指数和两个局部关联指标集，可以将其映射以指示关联强度的空间分布。本文附带了用于从矢量数据集计算所有索引的开源软件。为了展示V度量的效用，我们确定了三种不同的应用上下文：比较，关联和派生，并给出了每个示例的示例。与广泛使用的Mapcurves方法相比，V-measure方法具有多个优点，它在相互信息以及方差分析方面有清晰的解释，它提供了更精确的关联评估，可以通过以下方式随时使用随附的软件以及本文中提供的示例可作为其可能应用范围的指南。我们对V度量的重新分析产生了两个具体的贡献，即发现了地理探测器中的概念缺陷-一种量化数值和分类空间变量之间关联的方法，以及针对基于地图的新算法的建议聚类衍生的区域化中的最佳区域数。

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