# Spatial Performance Indicators for Traffic Flow Prediction
## 4 Results
### Comparison Between Different Clustering Scenarios
The star H scenario swaps these nodes into predetermined locations on the left and bottom left of the network, as shown in Figure 5. The results of these swaps not only create hotspots, but also possibly create coldspots or random spatial patterns that could reduce the \(G\) value. The question is which will have a greater impact on the network, as not all clusters are identical. If we compare Global Moran's I and Getis-Ord General G for star cluster scenarios, the ranking is similar, from highest to lowest: (1) star H, (2) star LL, (3) star HL, (4) star L, and (5) star HH. However, the impact of clusters compared to the original scenario is different between Global Moran's I and Getis-Ord General G. For Global Moran's I, all clustering scenarios increase their value, whereas, for Getis-Ord General G, hotspots increase their value and coldspots reduce their value. This trend is similar to the theoretical interpretation of both metrics: adding more hotspots will increase both metrics, but adding more coldspots will increase Global Moran's I and reduce Getis-Ord General G. These findings also support our assumption that clustering scenarios with swapping node procedures for a hotspot could result in a more impactful coldspot in other locations, thereby reducing the Getis-Ord General G.  
For the line cluster scenarios, the ranking of Getis-Ord General G is the opposite of that of Global Moran's I, and the effect of line clusters is the opposite of star clusters for Getis-Ord General G. This shows that the existence of both star and line clusters can cancel each other out, similar to how hotspots and coldspots cancel each other out. Table 6 summarizes the univariate analysis of the APAM values for all scenarios. We calculated APAM with \(\alpha=0.5\), assuming that the importance of the topology of the network and traffic flow data are equal. We calculated kurtosis using [PERSON]'s definition, with a positive kurtosis value representing leptokurtic, where the distribution has heavier tails and a higher peak. All the scenarios had positive skewness and kurtosis values. This means that the majority of the nodes have low APAM values, but some nodes have significantly higher APAM values. These nodes are highly important and can significantly affect the traffic networks. The variance of all clustering scenarios shows insignificant differences, and skewed distributions with high kurtosis render the variance of the distribution uninformative. Therefore, we did not further analyze the variance in the distribution. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & \(G\) & \(p_{G}\)**-Value** & \(z_{G}\)**-Score** \\ \hline Original & 0.0205 & 0.0273 & 1.9220 \\ Star H & 0.0245 & 0.0000 & 7.2793 \\ Star L & 0.0199 & 0.1276 & 1.1380 \\ Star HH & 0.0196 & 0.2373 & 0.7150 \\ Star LL & 0.0215 & 0.0006 & 3.2192 \\ Star HL & 0.0205 & 0.0313 & 1.8619 \\ Line H & 0.0199 & 0.1224 & 1.1631 \\ Line L & 0.0212 & 0.0021 & 2.8650 \\ Line HH & 0.0199 & 0.1371 & 1.0935 \\ Line LL & 0.0213 & 0.0013 & 3.0039 \\ Line HL & 0.0213 & 0.0016 & 2.9469 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Getis-Ord General G for each scenario. The star H is the most interesting scenario because of its significantly higher skewness and kurtosis. This indicates that the vast majority of nodes in star H have low importance, whereas a small minority have extraordinarily high importance. In the star H scenario, the hotspot is located within the center of the network, as shown in Figure 5. These nodes have high node value and centrality, resulting in significantly large APAM values, thereby increasing the skewness and kurtosis of the distribution. In other scenarios, the cluster is located in less connected areas, resulting in subtle changes in skewness and kurtosis values.