Graph Neural Networks (GNNs) have been broadly applied in many urban applications upon formulating a city as an urban graph whose nodes are urban objects like regions or points of interest. Recently, a few enhanced GNN architectures have been developed to tackle heterophily graphs where connected nodes are dissimilar. However, urban graphs usually can be observed to possess a unique spatial heterophily property; that is, the dissimilarity of neighbors at different spatial distances can exhibit great diversity. This property has not been explored, while it often exists. To this end, in this paper, we propose a metric, named Spatial Diversity Score, to quantitatively measure the spatial heterophily and show how it can influence the performance of GNNs. Indeed, our experimental investigation clearly shows that existing heterophilic GNNs are still deficient in handling the urban graph with high spatial diversity score. This, in turn, may degrade their effectiveness in urban applications. Along this line, we propose a Spatial Heterophily Aware Graph Neural Network (SHGNN), to tackle the spatial diversity of heterophily of urban graphs. Based on the key observation that spatially close neighbors on the urban graph present a more similar mode of difference to the central node, we first design a rotation-scaling spatial aggregation module, whose core idea is to properly group the spatially close neighbors and separately process each group with less diversity inside. Then, a heterophily-sensitive spatial interaction module is designed to adaptively capture the commonality and diverse dissimilarity in different spatial groups. Extensive experiments on three real-world urban datasets demonstrate the superiority of our SHGNN over several its competitors.

翻译：图神经网络（GNN）已广泛应用于众多城市应用中，其通过将城市建模为城市图，其中节点代表城市对象（如区域或兴趣点）。近年来，一些增强型图神经网络架构被开发出来以处理异质性图，即连接节点具有差异性的图。然而，城市图通常展现出独特的空间异质性特性：不同空间距离的邻居之间的差异性可能表现出极大的多样性。这一特性尽管普遍存在，却尚未被充分探索。为此，本文提出一种名为空间多样性分数的度量指标，用于定量衡量空间异质性，并展示其如何影响图神经网络的性能。实验研究明确表明，现有异质性图神经网络在处理高空间多样性分数的城市图时仍存在不足，这可能削弱其在城市应用中的有效性。基于此，我们提出一种面向空间异质性感知的图神经网络（SHGNN），以应对城市图中异质性的空间多样性问题。基于城市图中空间邻近邻居与中心节点呈现更相似差异模式的关键观察，我们首先设计了一个旋转-缩放空间聚合模块，其核心思想是合理分组空间邻近邻居，并分别处理各组以降低内部多样性。随后，设计了一个对异质性敏感的空间交互模块，以自适应捕捉不同空间组中的共性和多样化差异性。在三个真实世界城市数据集上的大量实验表明，我们的SHGNN相较于多个竞争模型具有优越性。