ABSTRACT

Few laws about geographical information are known, partly because geographical information is inherently complex. Tobler’s first law of Geography and, to a lesser degree, also his second law are among the rare exceptions. In this article, we explore the validity of Benford’s law in the context of the example of OpenStreetMap. More specifically, we compare the distribution of several numerical features of geographical entities to the Benford distribution. It is demonstrated that the numerical features examined are in accordance with Benford’s law to a varying degree with little variation between the types of geographical entities. Spatial patterns in the deviation from Benford’s law are shown to be similar for some aspects but to strongly differ for other ones. We show that many aspects of the data tend to deviate more than average from the Benford distribution in Africa, Greenland, smaller island countries, and, to a lesser degree, in South America. Also, the scale-dependency of Benford’s law is explored. Motivated by the use of Benford’s law to detect indications for fraud in economic and other datasets, future prospects and limitations to systematically develop intrinsic data quality measures are discussed.

摘要

很少有关于地理信息的法律为人所知，部分原因是地理信息本质上是复杂的。Tobler 的地理学第一定律以及在较小程度上还有他的第二定律都是极少数例外。在本文中，我们以 OpenStreetMap 为例探讨本福德定律的有效性。更具体地说，我们将地理实体的几个数字特征的分布与 Benford 分布进行了比较。结果表明，所检验的数值特征在不同程度上符合本福德定律，地理实体类型之间的差异很小。偏离本福德定律的空间模式在某些方面是相似的，但在其他方面却大不相同。我们表明，在非洲、格陵兰岛、小岛国，以及在较小程度上，在南美洲，数据的许多方面往往偏离本福德分布的平均水平。此外，还探讨了本福德定律的尺度依赖性。受使用 Benford 定律检测经济和其他数据集中的欺诈迹象的启发，讨论了系统开发内在数据质量措施的未来前景和局限性。