Beyond GeoFirst Law: Learning Spatial Representations via Integrated Autocorrelations and Complementarity 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 stepbystep SRL framework to integrate spatial autocorrelations and complementarity. This framework includes four testable steps. First, we construct multiview POIPOI(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 realworld real estate data to demonstrate the proposed method effectiveness.

Joint embedding of structure and features via graph convolutional networks The creation of social ties is largely determined by the entangled effects of peopleu0027s similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose emphAN2VEC, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared featurenetwork information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.