# Clustering of Road Traffic Accidents as a Gestalt Problem
## 4 Results
### Stability of Results through Time  
To estimate the stability of results through time, the introduced algorithm is applied to data collected in the same spatial area at different periods. The previous section considers the entire city of Belgrade, which has a surface area of approximately 3233 km\({}^{2}\). In this section, the same spatial threshold (i.e., \(\tau\) = 200 m) is applied to just one of the \"inner\" Belgrade municipalities--the municipality of Zvezdara--which has a surface area of approximately 31.11 km\({}^{2}\) (i.e., 9.6 percent of the city surface area). In line with our goal to introduce an approach suitable for application in circumstances of limited human or technical resources for traffic monitoring and management, this municipality was selected as one of the \"inner\" municipalities with fewest camera poles. It contains only 16 out of 464 camera poles installed in Belgrade. The algorithm is applied to publicly available data on traffic accidents with injuries or death that occurred in the municipality of Zvezdara over the three-year period from January 2019 to December 2021. The maps showing road traffic accidents that occurred in this municipality during 2021, 2020, and 2019 are given in Figure 4(a),c,e, respectively. The corresponding map representations of the selected clusters are given in Figure 4(b),d,f, respectively. The camera pole locations (March 2022) are represented for the purpose of completeness. A summary of the clustering and selection results is given in Table 3. The selected clusters are described in Table 4. \begin{table}
\begin{tabular}{l l c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Summary Data**} & **First Stage** & **Second Stage** \\  & & **(Clustering)** & **(Selection)** \\ \hline \multirow{4}{*}{2021} & Number of traffic accidents: & 317 & 116 \\  & Number of clusters: & 97 & 4 \\  & Average num. of accidents per cluster: & 3.186 & 29 \\  & Standard deviation: & 5.930 & 8.573 \\ \hline \multirow{4}{*}{2020} & Number of traffic accidents: & 282 & 101 \\  & Number of clusters: & 95 & 5 \\  & Average num. of accidents per cluster: & 2.905 & 20.2 \\  & Standard deviation: & 5.020 & 11.214 \\ \hline \multirow{4}{*}{2019} & Number of traffic accidents: & 349 & 136 \\  & Number of clusters: & 93 & 5 \\ \cline{1-1}  & Average num. of accidents per cluster: & 3.699 & 27.2 \\ \cline{1-1}  & Standard deviation: & 6.561 & 11.444 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: A summary of the clustering and selection results obtained when the introduced algorithm was applied to publicly available data on traffic accidents with injuries or death that occurred in the municipality of Zvezdara during 2021, 2020, and 2019, respectively. Figure 5: _Cont._ \begin{table}
\begin{tabular}{c l c c c c c} \hline \hline  & Cluster ID: & 161 & 22 & 198 & 78 & \\
**2021** & Number of Traffic Accidents: & 43 & 28 & 25 & 20 & \\  & Area (km\({}^{2}\)): & 0.132 & 0.193 & 0.171 & 0.189 & \\ \hline  & Cluster ID: & 28 & 5 & 6 & 140 & 182 \\
**2020** & Number of Traffic Accidents: & 42 & 19 & 16 & 12 & 12 \\  & Area (km\({}^{2}\)): & 0.272 & 0.073 & 0.065 & 0.121 & 0.109 \\ \hline  & Cluster ID: & 194 & 72 & 192 & 116 & 80 \\
**2019** & Number of Traffic Accidents: & 50 & 23 & 22 & 21 & 20 \\  & Area (km\({}^{2}\)): & 0.486 & 0.235 & 0.317 & 0.163 & 0.145 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Description of the selected clusters obtained when the introduced algorithm was applied to publicly available data on traffic accidents with injuries or death that occurred in the municipality of Zvezdara during 2021, 2020, and 2019, respectively. The stability of results through time is considered in two aspects: the share of traffic accidents belonging to the selected clusters, and the overlapping surface area between the selected clusters in all three years.