# Spatial Performance Indicators for Traffic Flow Prediction
## 4 Results
### Comparison Between Different Clustering Scenarios  
To analyze the capabilities of spatial KPIs, we created 10 different clustering scenarios by swapping node values to create artificial hotspots or coldspots. The Global Moran's I values for all the scenarios are summarized in Table 4. All scenarios had significant \(p_{I}\)-values and positive \(z_{I}\)-scores, indicating a positive spatial autocorrelation. Compared to the original STSGCN results, all scenarios have higher \(z_{I}\)-scores, indicating that the existence of clusters increases the spatial autocorrelation of the network. This finding indicates that a larger value of \(I\) can signal clustering in the network. Hotspot scenarios, except for Star HH, have a higher spatial autocorrelation than their coldspot counterparts. Figure 6 shows that high-value nodes are less common than low-value nodes and are more sporadic. The hotspot clustering scenario transforms the sporadic pattern into a cluster, thereby significantly increasing the spatial autocorrelation. The results also show that line clusters exhibit a clearer difference between hotspots and coldspots compared to star clusters. Line HL shows the largest \(G\), further indicating that the Global Moran's I is more sensitive to line clusters. Based on these findings, Global Moran's I can detect an increase in spatial autocorrelation caused by clustering scenarios. In addition to spatial autocorrelation, it is important to determine the type of cluster that appears in traffic prediction results. If hotspots are more dominant, then a large spatial autocorrelation is detrimental to the network, as this suggests locations with a large systematic error. However, the dominant coldspots suggest that spatial relationships are well-captured by traffic prediction methods. This leads us to the second proposed spatial KPIs, Getis-Ord General G, which measures the spatial clustering of high- or low-value nodes. The Getis-Ord General G values for all the scenarios are summarized in Table 5. All scenarios, except star L, star HH, line H, and line HH, showed significant \(p_{G}\)-values with positive \(z_{G}\)-scores, indicating the spatial clustering of high node values. The four mentioned scenarios have \(p_{G}\)-values larger than 0.05, so the null hypothesis cannot be rejected, and there is no tendency between hotspots or coldspots. An interesting aspect of these results is that hotspot scenarios do not generally increase the \(G\) value, and vice versa, as [PERSON] stated. Of all hotspot scenarios, only the \(G\) value of Star H increased, but the value increased significantly. On the other hand, all coldspot scenarios, except Star L, have increasing \(G\) values. However, in all cases, hotspots \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & \(\mathbf{I}\) & \(\mathbf{p_{I}}\)**-Value** & \(\mathbf{z_{I}}\)**-Score** \\ \hline Original & 0.1690 & 0.0086 & 2.6286 \\ Star H & 0.3316 & 0.0000 & 5.0705 \\ Star L & 0.2557 & 0.0001 & 3.9302 \\ Star HH & 0.2115 & 0.0011 & 3.2661 \\ Star LL & 0.2799 & 0.0000 & 4.2942 \\ Star HL & 0.2659 & 0.0000 & 4.0838 \\ Line H & 0.3671 & 0.0000 & 5.6044 \\ Line L & 0.2125 & 0.0010 & 3.2811 \\ Line HH & 0.3364 & 0.0000 & 5.1421 \\ Line LL & 0.2056 & 0.0015 & 3.1770 \\ Line HL & 0.4337 & 0.0000 & 6.6051 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Global Moran’s I for each scenario. and coldspots always had opposite effects on the \(G\) value. For example, line H had a decreasing \(G\) value, whereas line L had an increasing \(G\) value. This finding suggests that hotspots and coldspots have opposite effects, and the existence of both might cancel each other out. The clustering scenarios, such as star HH, show two obvious hotspots on the left and bottom left of the network if we inspect it visually in Figure 7. However, the \(p_{G}\)-value is not significant so it does not have a tendency for hotspots or coldspots. If we inspect the original scenario (Figure 6), we can see that most of the high-value nodes are scattered.