# Spatial Performance Indicators for Traffic Flow Prediction
## 5 Discussion  
In this study, we propose three different spatial KPIs that measure the performance of traffic flow prediction: (1) spatial autocorrelation (Global Moran's I), (2) spatial clustering of node values (Getis-Ord General G), and (3) node centrality measure (Adapted PageRank Algorithm Modified). We considered 10 clustering scenarios created by swapping node values to demonstrate the ability of spatial KPIs to evaluate traffic prediction methods that have identical average RMSE. We also validated these spatial KPIs against four different traffic prediction methods: (1) STSGCN [7], (2) ASTGCN [6], (3) DDGCRN [20], and (4) STAEformer [21] to predict traffic flow from the PeMSD8 dataset [19]. If we only consider the average RMSE (shown in Table 3), it is clear that STAEformer has the lowest average RMSE. However, the difference between STAEformer and DDGCRN is small, and the performance might vary from one network to another; hence, there is a need for other measures to evaluate traffic flow prediction methods. A similar case also occurs between STSGCN and ASTGCN, which have similar average RMSE values. For cases in which the standard prediction accuracy between different methods has negligible differences, our results show that spatial KPIs can provide extra information based on the spatial characteristics of the methods. Global Moran's I results show that spatial clusters increased spatial autocorrelation, with hotspots giving a larger impact compared to coldspots. We also found that line clusters had a higher impact than star clusters. Based on this finding, a lower value of Global Moran's I is preferred, owing to less spatial clustering (especially hotspots) in the network. A prediction model with less spatial clustering (\(I\) close to zero) is preferred due to its consistent performance across the network. All traffic prediction methods showed positive spatial autocorrelation with subtle differences between the methods, which made this metric less informative in our case study. Traffic flow and RMSE have a linear relationship, so positive spatial autocorrelation is unavoidable. However, the results signal a relationship between spatial autocorrelation and spatial information utilized by traffic prediction methods. In the clustering scenarios, Getis-Ord General G shows nuanced results, where the hotspot scenarios do not always increase \(G\), and vice versa, because of swapping in the clustering scenarios. In general, a lower value of \(z_{G}\)-score is preferred from the traffic flow prediction error because it suggests spatial clustering of low RMSE nodes, which implies the prediction model performs well in connected areas. The results show that Getis-Ord General G can capture spatial clustering that is not easily discernible through visual inspection. For example, in the original scenario, the \(p_{G}\)-value is significant with a positive \(z_{G}\)-score, which indicates the spatial clustering of high node values. However, it is difficult to determine where the hotspot is located if we inspect Figure 6. It is important to note that the results show that hotspots and coldspots cancel each other. This also occurs between star and line clusters. Getis-Ord General G was able to show a clear difference between ASTGCN and STSGCN, which have similar average RMSE and utilize the graph adjacency matrix, demonstrating the capability of this KPI to differentiate traffic prediction method. The results show that ASTGCN showed no spatial clustering tendencies, which is preferred over STSGCN, which has a spatial clustering of high node values. For the APAM univariate analysis, extreme clustering scenarios such as Star H, a cluster consisting of highly important nodes with high node centrality and node values, can be detected from the skewness and kurtosis values. Nodes of high importance require attention owing to their significant effects on traffic networks. Traffic prediction methods with fewer numbers of such nodes were preferred.