This article introduces a novel low rank approximation (LRA)-based model to detect the functional regions with the data from about 15 million social media check-in records during a year-long period in Shanghai, China. We identified a series of latent structures, named latent spatio-temporal activity structures. While interpreting these structures, we can obtain a series of underlying associations between the spatial and temporal activity patterns. Moreover, we can not only reproduce the observed data with a lower dimensional representative, but also project spatio-temporal activity patterns in the same coordinate system. With the K-means clustering algorithm, five significant types of clusters that are directly annotated with a combination of temporal activities can be obtained, providing a clear picture of the correlation between the groups of regions and different activities at different times during a day. Besides the commercial and transportation dominant areas, we also detected two kinds of residential areas, the developed residential areas and the developing residential areas. We further interpret the spatial distribution of these clusters using urban form analytics. The results are highly consistent with the government planning in the same periods, indicating that our model is applicable to infer the functional regions from social media check-in data and can benefit a wide range of fields, such as urban planning, public services, and location-based recommender systems.