Fast Identification of Urban Sprawl Based on K-Means Clustering with Population Density and Local Spatial Entropy

As urban sprawl is proven to jeopardize the sustainability system of cities, the identification of urban sprawl is essential for urban studies. Compared with previous related studies which tend to utilize more and more complicated variables to recognize urban sprawl while still retaining an element of uncertainty, this paper instead proposes a simplified model to identify urban sprawl patterns. This is a working theory which is based on a diagram interpretation of the classic urban spatial structure patterns of the Chicago School. The method used in our study is K-means clustering with gridded population density and local spatial entropy. The results and comparison with open population data and mobile phone data verify the assumption and furthermore indicate that the accuracy of source population data will limit the precision of output identification. This article concludes that urban sprawl is mainly dominated by population and surrounding unevenness. Moreover, the Floating Catchment Area (FCA) local spatial entropy method presented in this research brings about an integration of Shannon entropy, Tobler’s first law of geography and the Moore neighborhood, improving the spatial homogeneity and locality of Batty’s Spatial Entropy model which can only be used in a general scope.