  Most existing literature focuses on the exterior temporal rhythm of human
movement to infer the functional regions in a city, but they neglects the
underlying interdependence between the functional regions and human activities
which uncovers more detailed characteristics of regions. In this research, we
proposed a novel model based on the low rank approximation (LRA) to detect the
functional regions using the data from about 15 million check-in records during
a yearlong period in Shanghai, China. We find a series of latent structures,
called urban spatial-temporal activity structure (USTAS). While interpreting
these structures, a series of outstanding underlying associations between the
spatial and temporal activity patterns can be found. Moreover, we can not only
reproduce the observed data with a lower dimensional representative but also
simultaneously project both the spatial and temporal activity patterns in the
same coordinate system. By utilizing the K-means clustering algorithm, five
significant types of clusters which are directly annotated with a corresponding
combination of temporal activities can be obtained. This provides a clear
picture of how the groups of regions are associated with different activities
at different time of day. Besides the commercial and transportation dominant
area, we also detect two kinds of residential areas, the developed residential
areas and the developing residential areas. We further verify the spatial
distribution of these clusters in the view of urban form analysis. The results
shows a high consistency with the government planning from the same periods,
indicating our model is applicable for inferring the functional regions via
social media check-in data, and can benefit a wide range of fields, such as
urban planning, public services and location-based recommender systems and
other purposes.
