# Towards Robust Representations of Spatial Networks Using Graph Neural Networks
## 6 Conclusions  
In this article, we have studied the problem of data representations for the semantic inference of spatial networks using Graph Neural Networks. Based on the fact that data representations impact the performance of a machine learning model [2], we seek to explore the link between data representation and model performance. We argue that the expressive nature of heterogeneous graph representations of spatial networks offers richer structural and semantic information which may improve model performance for certain tasks than their homogeneous counterparts. We focus on street type and building type inference problems in spatial networks. Our empirical evaluations show that heterogeneous graph \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Dataset** & **Split** & **GCN** & **GAT** & **GraphSAGE** & **HetSpatial** \\ \hline \multirow{4}{*}{**Dublin**} & 20\% & 0.92 \(\pm\) 0.013 & **0.94**\(\pm\) 0.013 & 0.93 \(\pm\) 0.011 & 0.93 \(\pm\) 0.007 \\  & 40\% & 0.93 \(\pm\) 0.010 & **0.94**\(\pm\) 0.008 & 0.93 \(\pm\) 0.009 & 0.93 \(\pm\) 0.006 \\  & 50\% & 0.95 \(\pm\) 0.008 & **0.96**\(\pm\) 0.008 & 0.93 \(\pm\) 0.009 & 0.93 \(\pm\) 0.005 \\  & 70\% & 0.92 \(\pm\) 0.012 & **0.95**\(\pm\) 0.008 & 0.93 \(\pm\) 0.009 & 0.93 \(\pm\) 0.004 \\ \hline \multirow{4}{*}{**Frankfurt**} & 20\% & 0.73 \(\pm\) 0.023 & 0.80 \(\pm\) 0.013 & **0.81**\(\pm\) 0.023 & 0.69 \(\pm\) 0.02 \\  & 40\% & 0.77 \(\pm\) 0.022 & 0.80 \(\pm\) 0.02 & **0.82**\(\pm\) 0.021 & 0.69 \(\pm\) 0.024 \\  & 50\% & 0.74 \(\pm\) 0.031 & 0.81 \(\pm\) 0.028 & **0.82**\(\pm\) 0.017 & 0.70 \(\pm\) 0.026 \\  & 70\% & 0.75 \(\pm\) 0.020 & **0.83**\(\pm\) 0.025 & 0.82 \(\pm\) 0.017 & 0.70 \(\pm\) 0.018 \\ \hline \multirow{4}{*}{**Toronto**} & 20\% & 0.90 \(\pm\) 0.013 & 0.91 \(\pm\) 0.011 & 0.92 \(\pm\) 0.009 & **0.96**\(\pm\) 0.006 \\  & 40\% & 0.87 \(\pm\) 0.013 & 0.86 \(\pm\) 0.016 & 0.93 \(\pm\) 0.012 & **0.96**\(\pm\) 0.006 \\  & 50\% & 0.89 \(\pm\) 0.014 & 0.84 \(\pm\) 0.014 & 0.92 \(\pm\) 0.012 & **0.96**\(\pm\) 0.005 \\  & 70\% & 0.86 \(\pm\) 0.016 & 0.92 \(\pm\) 0.009 & 0.93 \(\pm\) 0.009 & **0.96**\(\pm\) 0.007 \\ \hline \multirow{4}{*}{**Manchester**} & 20\% & 0.86 \(\pm\) 0.078 & 0.84 \(\pm\) 0.064 & **0.87**\(\pm\) 0.077 & 0.73 \(\pm\) 0.085 \\  & 40\% & 0.85 \(\pm\) 0.076 & **0.90**\(\pm\) 0.072 & 0.85 \(\pm\) 0.077 & 0.71 \(\pm\) 0.066 \\  & 50\% & **0.95**\(\pm\) 0.040 & 0.90 \(\pm\) 0.070 & 0.94 \(\pm\) 0.058 & 0.71 \(\pm\) 0.057 \\  & 70\% & 0.90 \(\pm\) 0.088 & **0.94**\(\pm\) 0.064 & 0.86 \(\pm\) 0.075 & 0.70 \(\pm\) 0.074 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Table showing the micro F1-score results for building type inference. The values in bold and underlined represent the best and second best performing approaches for each city/split, respectively. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Dataset** & **Split** & **GCN** & **GAT** & **GraphSAGE** & **HetSpatial** \\ \hline \multirow{4}{*}{**Dublin**} & 20\% & **0.75**\(\pm\) 0.005 & 0.62 \(\pm\) 0.008 & **0.75**\(\pm\) 0.005 & 0.72 \(\pm\) 0.180 \\  & 40\% & 0.75 \(\pm\) 0.006 & 0.59 \(\pm\) 0.008 & 0.75 \(\pm\) 0.009 & **0.79**\(\pm\) 0.247 \\  & 50\% & **0.75**\(\pm\) 0.006 & 0.58 \(\pm\) 0.008 & **0.75**\(\pm\) 0.007 & 0.70 \(\pm\) 0.251 \\  & 70\% & 0.74 \(\pm\) 0.006 & 0.62 \(\pm\) 0.006 & 0.75 \(\pm\) 0.006 & **0.78**\(\pm\) 0.180 \\ \hline \multirow{4}{*}{**Frankfurt**} & 20\% & 0.71 \(\pm\) 0.013 & 0.57 \(\pm\) 0.013 & **0.73**\(\pm\) 0.017 & 0.72 \(\pm\) 0.180 \\  & 40\% & 0.73 \(\pm\) 0.010 & 0.59 \(\pm\) 0.021 & 0.73 \(\pm\) 0.013 & **0.75**\(\pm\) 0.199 \\  & 50\% & 0.72 \(\pm\) 0.012 & 0.62 \(\pm\) 0.013 & 0.73 \(\pm\) 0.0 representations may indeed be better suited for the street type inference problem than the homogeneous graph representation.