## 6 Experimental Evaluation
### Evaluation with Aggregate Privacy Attack
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Metrics** & **Mean** & **Standard Deviation** \\ \hline Reidentified Total & \(\varepsilon=\) & 1 & 1.5 \\  & 1.5 & 1.78 & 0.44 \\  & 2 & 0.78 & 0.44 \\ \hline \multirow{2}{*}{Non-Reidentified Total} & \(\varepsilon=\) & 1 & 535 & 0.5 \\  & 1.5 & 534.22 & 0.44 \\  & 2 & 535.22 & 0.44 \\ \hline \multirow{2}{*}{Reidentified (\%)} & \(\varepsilon=\) & 1 & 0.19 & 0.09 \\  & 1.5 & 0.33 & 0.08 \\  & 2 & 0.15 & 0.08 \\ \hline \multirow{2}{*}{Non-Reidentified (\%)} & \(\varepsilon=\) & 1 & 99.81 & 0.09 \\  & 1.5 & 99.67 & 0.08 \\  & 2 & 99.85 & 0.08 \\ \hline \multirow{2}{*}{Average Distance (Topsee Div.)} & 1 & 0.162 & 0.016 \\  & 1.5 & 0.144 & 0.015 \\  & 2 & 0.139 & 0.016 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: HMC-obfuscated synthetic dataset—overview. To maintain consistency, randomness is controlled by setting nine pre-defined NumPy _np.random_ seeds, which ensure that the same random trajectories are used across trials. Each scenario is conducted over nine separate trials, ensuring consistent and reliable results by reducing the influence of random variations in the data partitioning process. The following terms explain the metrics used in the results tables:  
* **(Non-)Reidentified Total:** This refers to the total number of (un-)successful reidentifications. * **(Non-)Reidentified (%):** This refers to the percentage of (un-)successful reidentifications. * **Seed:** NumPy seed set with _np.random_. This influences how the datasets are partitioned into train and test datasets. * **Average Distance:** The average minimum distance determined by calculating Topsoe Divergence--see Equation (1)--over all 536 datasets. Table 1 provides an overview of the non-obfuscated dataset, summarizing key metrics across all trials. It includes the average reidentification rate (19.2%) and its standard deviation of 6.12, along with the corresponding non-reidentification rate (80.8%). The mean Topsoe Divergence is 0.034, and its standard deviation is 0.014. These values function as the baseline for comparing the effectiveness of the obfuscation process. The detailed results as shown in Table 1 exhibit a **Reidentified (%)** rate ranging from 8.40% to 28.36%. This highlights the significant risk associated with sharing raw mobility data, as nearly one in five mobility traces can be successfully reidentified without any privacy protection measures. The **Average Distance** measured as a Topsoe Divergence shows some variance with values ranging from 0.02 to 0.07. In contrast, the HMC-obfuscated dataset, as shown in Tables 2 and 2, achieves a substantial reduction in reidentification rates. Compared to Table 1, the average reidentification rate decreases from 19.2% to 1.76%, demonstrating the effectiveness of HMC in enhancing privacy protection. The corresponding non-reidentification rate increases from 80.8% in the non-obfuscated dataset to 98.24% in the HMC-obfuscated dataset. The **Reidentified (%)** rate in HMC (Table 2) ranges from 0.56% to 2.5%, with an average significantly lower than in the non-obfuscated dataset. The lowest reidentification rate appears in Trial 4 (0.56%), while the highest (2.5%) occurs in Trial 1 and Trial 6. The **Average Distance (Topsoe Divergence)** values for the HMC dataset range from 0.05 to 0.10, which is a bit over the value of the non-obfuscated dataset. This suggests that HMC alone effectively increases anonymity and reduces the likelihood of reidentification. In contrast, the HMC-obfuscated synthetic dataset, shown in Tables 3 and 3, achieves an even greater reduction in reidentification rates. Compared to Table 1, the average reidentification rate drops from 19.2% in the non-obfuscated dataset to just 0.15% to 0.33% in the HMC-obfuscated synthetic dataset, depending on the \(\varepsilon\) used. The non-reidentification rate increases correspondingly from 99.85% to 99.67%, indicating that the combination of HMC and LDPTrace provides strong privacy protection.