Tobler’s first law of geography is widely recognized as reflecting broad empirical realities in geography. Its key concepts of “near” and “related” are intuitive in a univariate setting. However, when moving to the joint consideration of spatial patterns among multiple variables, the combination of attribute similarity and geographical similarity that underlies the concept of spatial autocorrelation is much harder to deal with. This article uses the notion of distance in multiattribute space to explore and visualize the connection between “near” and “related” in a multivariate context. We approach this from a global, local, and regional perspective. We outline a number of ways to combine different visualization techniques and introduce a new local neighbor match test for multivariate local clusters. We illustrate the methods by means of Guerry’s classic data set on moral statistics in 1833 France.

中文翻译：

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多元世界中的托伯定律

托伯勒的地理第一定律被广泛认为反映了地理上广泛的经验现实。在单变量设置中，其“附近”和“相关”的关键概念很直观。但是，当考虑多个变量之间的空间模式的联合考虑时，要解决空间自相关概念的属性相似度和地理相似度的组合就很难处理了。本文使用多属性空间中的距离概念来探索和可视化多变量上下文中“附近”和“相关”之间的联系。我们从全球，本地和区域的角度来解决这个问题。我们概述了多种方法来组合不同的可视化技术，并为多元本地聚类引入新的本地邻居匹配测试。