Inspired by Christopher Alexander's conception of the world - space is not lifeless or neutral, but a living structure involving far more small things than large ones - a topological representation has been previously developed to characterize the living structure or the wholeness of geographic space. This paper further develops the topological representation and living structure for predicting human activities in geographic space. Based on millions of street nodes of the United Kingdom extracted from OpenStreetMap, we established living structures at different levels of scale in a nested manner. We found that tweet locations at different levels of scale, such as country and city, can be well predicted by the underlying living structure. The high predictability demonstrates that the living structure and the topological representation are efficient and effective for better understanding geographic forms. Based on this major finding, we argue that the topological representation is a truly multiscale representation, and point out that existing geographic representations are essentially single scale, so they bear many scale problems such as modifiable areal unit problem, the conundrum of length and the ecological fallacy. We further discuss on why the living structure is an efficient and effective instrument for structuring geospatial big data, and why Alexander's organic worldview constitutes the third view of space.

Capturing and characterizing collective human activities in a geographic space have become much easier than ever before in the big era. In the past few decades it has been difficult to acquire the spatiotemporal information of human beings. Thanks to the boom in the use of mobile devices integrated with positioning systems and location-based social media data, we can easily acquire the spatial and temporal information of social media users. Previous studies have successfully used street nodes and geo-tagged social media such as Twitter to predict users’ activities. However, whether human activities can be well represented by social media data remains uncertain. On the other hand, buildings or architectures are permanent and reliable representations of human activities collectively through historical footprints. This study aims to use the big data of US building footprints to investigate the reliability of social media users for human activity prediction. We created spatial clusters from 125 million buildings and 1.48 million Twitter points in the US. We further examined and compared the spatial and statistical distribution of clusters at both country and city levels. The result of this study shows that both building and Twitter data spatial clusters show the scaling pattern measured by the scale of spatial clusters, respectively, characterized by the number points inside clusters and the area of clusters. More specifically, at the country level, the statistical distribution of the building spatial clusters fits power law distribution. Inside the four largest cities, the hotspots are power-law-distributed with the power law exponent around 2.0, meaning that they also follow the Zipf’s law. The correlations between the number of buildings and the number of tweets are very plausible, with the r square ranging from 0.53 to 0.74. The high correlation and the similarity of two datasets in terms of spatial and statistical distribution suggest that, although social media users are only a proportion of the entire population, the spatial clusters from geographical big data is a good and accurate representation of overall human activities. This study also indicates that using an improved method for spatial clustering is more suitable for big data analysis than the conventional clustering methods based on Euclidean geometry.

Urban structure can be better comprehended through analyzing its cores. Geospatial big data facilitate the identification of urban centers in terms of high accuracy and accessibility. However, previous studies seldom leverage multi-source geospatial big data to identify urban centers from a topological perspective. This study attempts to identify urban centers through the spatial integration of multi-source geospatial big data, including nighttime light imagery (NTL), building footprints (BFP) and street nodes of OpenStreetMap (OSM). We use a novel topological approach to construct complex networks from intra-urban hotspots based on the theory of centers by Christopher Alexander. We compute the degree of wholeness value for each hotspot as the centric index. The overlapped hotspots with the highest centric indices are regarded as urban centers. The identified urban centers in New York, Los Angeles, and Houston are consistent with their downtown areas, with overall accuracy of 90.23%. In Chicago, a new urban center is identified considering a larger spatial extent. The proposed approach can effectively and objectively prevent counting those hotspots with high intensity values but few neighbors into the result. This study proposes a topological approach for urban center identification and a bottom-up perspective for sustainable urban design.