## 6 Experimental Evaluation
### Evaluation with Aggregate Privacy Attack  
To test how well HMC and LDPTrace protect data, we apply an AP-Attack in two steps:  
* AP-Attack on unaltered Heat Maps: The AP-Attack is first applied to the original heat maps, which have not been anonymized with HMC. This provides a baseline reidentification rate, showing how easily a taxi can be reidentified without any further anonymization. * AP-Attack on obfuscated Heat Maps: The AP-Attack is applied to the heat maps after the HMC anonymization process. Comparing the reidentification rates from the original and altered maps shows whether the HMC process is effective. A lower reidentification rate indicates successful anonymization. In both cases, tests are conducted with synthesized trajectories (created with LDPTrace, based on the San Francisco Cabspotting dataset) and non-synthesized trajectories (the original trajectories from the San Francisco Cabspotting dataset). This allows us to compare how well the different approaches perform under varying circumstances. The results of the AP-Attacks performed on the San Francisco Cabspotting dataset are presented in Tables 1 and 2 for the non-obfuscated baseline data and the data processed with HMC. In contrast, Tables 3 and 4 display the outcomes when using synthesized trajectories generated by LDPTrace. While Tables 1-4 summarize the average values and standard deviations across all trials, Tables A1-A4 in Appendix A provide a detailed breakdown of nine individual trials. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Metrics** & **Mean** & **Standard Deviation** \\ \hline Reidentified Total & 103 & 32.784 \\ Non-Reidentified Total & 433 & 32.784 \\ \hline Reidentified (\%) & 19.20 & \\ Non-Reidentified (\%) & 80.80 & 6.116 \\ \hline Average Distance & 0.034 & 0.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Non-obfuscated normal dataset—overview. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Metrics** & **Mean** & **Standard Deviation** \\ \hline Reidentified Total & \(\varepsilon=\) & 1 & 1.67 & 0.71 \\  & 1.5 & 2.56 & 0.73 \\  & 2 & 1.33 & 0.5 \\ \hline Non-Reidentified Total & \(\varepsilon=\) & 1 & 534.33 & 0.71 \\  & 1.5 & 533.33 & 0.73 \\  & 2 & 534.67 & 0.5 \\ \hline Reidentified (\%) & \(\varepsilon=\) & 1 & 0.31 & 0.13 \\  & 1.5 & 0.48 & 0.14 \\  & 2 & 0.24 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Non-obfuscated synthetic dataset—overview. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Metrics** & **Mean** & **Standard Deviation** \\ \hline Reidentified Total & 103 & 32.784 \\ \hline Reidentified (\%) & 19.20 & 6.116 \\ \hline Average Distance (Topsee Divergence) & 0.034 & 0.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Non-obfuscated normal dataset—overview. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Metrics** & **Mean** & **Standard Deviation** \\ \hline Reidentified Total & \(\varepsilon=\) & 1 & 1.67 & 0.71 \\  & 1.5 & 2.56 & 0.73 \\  & 2 & 1.33 & 0.5 \\ \hline \hline \multirow{2}{*}{Non-Reidentified Total} & \(\varepsilon=\) & 1 & 534.33 & 0.71 \\  & 1.5 & 533.33 & 0.73 \\  & 2 & 534.67 & 0.5 \\ \hline \hline \multirow{2}{*}{Reidentified (\%)} & \(\varepsilon=\) & 1 & 0.31 & 0.13 \\  & 1.5 & 0.48 & 0.14 \\  & 2 & 0.24 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: HMC-obfuscated normal dataset—overview.