# Towards Robust Representations of Spatial Networks Using Graph Neural Networks
## 2 Background  
Our study seeks to address the semantic inference problem in spatial networks. We discuss machine learning approaches to this problem. [PERSON] et al. [6] attempt to predict the semantics of streets on OpenStreetMap using the street geometries. They focus on inferring street types, using geometric properties such as length and linearity. The street segments are modelled as graphs and a Markov random field model is used to perform inference. They use data from Boston, achieving 68% precision and 65% recall on the classification tasks. [PERSON] and [PERSON] [5] develop machine learning models using contextual information to predict the semantics of streets on OpenStreetMap. They define contextual information as the type of objects that lie within the neighbourhood of a street. Similarly, they focus on street types as the semantics of the streets. They train tree-based models to perform inference. [PERSON] et al. [17] developed both weakly-supervised and semi-supervised machine learning models for building maps. They focus on building detection and road segmentation. Their models achieve improved performance by using data collected from OpenStreetMap. [PERSON] and [PERSON] [7] proposed the use of transfer learning to develop transferable models to mitigate the data availability problem for enriching spatial semantics. Using a statistical multi-measure, they are able to determine apriori the suitability of a model for a domain.  
Our work in this article focuses on Graph Neural Networks (GNNs) which are a type of Artificial Neural Networks designed to work on graphs. GNNs can be broadly classified into spectral and spatial approaches. Spectral GNNs derive object representations through operations on the graph Laplacian matrix, which could be very expensive to compute, thereby affecting scalability [18; 19; 20; 21]. Spatial GNNs derive representations directly from the graph, operating on spatially close neighbours of a graph object [22; 23]. Graph Neural Networks (GNNs) are capable of encoding the relational inductive bias in structures, hereby addressing a limitation of standard machine learning methods [7; 9; 24; 25]. This capability has been leveraged to improve model performance. [PERSON] et al. [26] proposed a hybrid neural architecture that is comprised of a Convolutional Neural Network (CNNs) and a Graph Neural Network (GNN). Their architecture is targeted at inferring the attributes of street networks. Their evaluations show that incorporating the GNN allows their architecture to mitigate the receptive field limitation of CNNs. [PERSON] and [PERSON] [8] develop effective Graph Neural Network models to infer spatial semantics using a node importance sampling technique. Their technique enables the GNN to outperform vanilla GNNs on the street semantics inference task. However, they focus on homogeneous graph representations, whereas, heterogeneous graph representations could offer a richer representation of data and improve model performance [4]. Our work in this article extends the applications of GNNs to the semantic inference of spatial networks using heterogeneous graph representations. We can also classify Graph Neural Networks based on the type of graph representations they are designed to work on as: _Homogeneous Graph Neural Networks_ and _Heterogeneous Graph Neural Networks_. Similar to our earlier definitions of homogeneous and heterogeneous graph representations, a graph neural network is said to be homogeneous if it is designed to work on homogeneous graph representations and heterogeneous if it is designed to work on heterogeneous graph representations. GCN [19], GAT [23], GraphSAGE [22] are some examples of Homogeneous GNNs while HetGCN [27] and HAN [28] are some examples of Heterogeneous GNNs. We study both homogeneous and heterogeneous GNNs in this paper, in order to understand the relationship between model performance and data representations.