Urban regions are places where people live, work, consume, and entertain. In this study, we investigate the problem of learning an embedding space for regions. Studying the representations of regions can help us to better understand the patterns, structures, and dynamics of cities, support urban planning, and, ultimately, to make our cities more livable and sustainable. While some efforts have been made for learning the embeddings of regions, existing methods can be improved by incorporating locality-constrained spatial autocorrelations into an encode-decode framework. Such embedding strategy is capable of taking into account both intra-region structural information and inter-region spatial autocorrelations. To this end, we propose to learn the representations of regions via a new embedding strategy with awareness of locality-constrained spatial autocorrelations. Specifically, we first construct multi-view (i.e., distance and mobility connectivity) POI-POI networks to represent regions. In addition, we introduce two properties into region embedding: (i) spatial autocorrelations: a global similarity between regions; (ii) top-k locality: spatial autocorrelations locally and approximately reside on top k most autocorrelated regions. We propose a new encoder-decoder based formulation that preserves the two properties while remaining efficient. As an application, we exploit the learned embeddings to predict the mobile checkin popularity of regions. Finally, extensive experiments with real-world urban region data demonstrate the effectiveness and efficiency of our method.

Spatial representation learning (SRL) is to automatically learn feature representations that characterize spatial entities. In this paper, we study the problem of improving spatial representation learning using spatial structure knowledge. We consider two types of structure knowledge: (1) spatial autocorrelations refer to the pattern that similar spatial entities are more likely to share similar roles and configurations. (2) spatial complementarity refers to the effect that the role of a spatial entity can be complemented and augmented by other different yet compatible spatial entities. Along this line, we develop a step-by-step SRL framework to integrate spatial autocorrelations and complementarity. This framework includes four testable steps. First, we construct multi-view POI-POI(Point of Interest) graphs to characterize the static and dynamic patterns of each spatial region. We then use the graphs as inputs to train an adversarial autoencoder (AAE) that can preserve the spatial autocorrelation property and learn representations of spatial entities. Later, with the learned representations extracted from AAE inputs, a Graph Convolutional Network (GCN) is trained in an unsupervised fashion in order to overcome label sparsity and capture the spatial complementarity effect. In this way, we significantly improve the quality of spatial representations. In addition, we apply the proposed method to characterize residential communities for predicting real estate prices. Finally, we present intensive experimental results with real-world real estate data to demonstrate the proposed method effectiveness.