A novel method is proposed to define cities' boundaries within a given national urban system. Point Volunteered Geographic Information, such as the OpenStreetMap road network nodes, together with national geospatial information, like economic units, are recursively clustered using DBSCAN at different distance thresholds; clusters smaller than a threshold reflecting the rural settlements pattern are filtered, and then Shannon's entropy for the entire system is calculated. The system of percolated nodes obtained when this entropy reaches its maximum is compared against the current definition of what is officially urban. It is found to be very similar to the actual urban-nonurban classification, and also to have a very high correspondence with the current classification of the Mexican National Urban System (SUN). An additional finding is that the percolated system at the maximum entropy value has a very high correspondence with Zipf's law, while the current Mexican SUN does not.

中文翻译：

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通过 DBSCAN 和香农熵定义城市边界：墨西哥国家城市系统案例

提出了一种新方法来定义给定国家城市系统内的城市边界。点志愿地理信息（例如 OpenStreetMap 道路网络节点）与国家地理空间信息（例如经济单位）一起使用 DBSCAN 在不同距离阈值下进行递归聚类；过滤掉小于反映农村聚落模式阈值的聚类，然后计算整个系统的香农熵。将熵达到最大值时获得的渗透节点系统与当前官方城市的定义进行比较。人们发现它与实际的城市-非城市分类非常相似，并且与墨西哥国家城市系统（SUN）当前的分类具有非常高的对应性。另一个发现是，最大熵值处的渗透系统与齐普夫定律具有非常高的对应性，而当前的墨西哥太阳却没有。