## 6 Experiments
### Selecting Background Knowledge Configurations with Low-Entropy Feature Frequency
#### 6.5.3 Foursquare  
In the next experiments, we explored the examination of the Foursquare dataset. Our primary aim was to analyze the distribution of re-identification risk and assess the potential impact of targeting low entropy and feature frequency within background knowledge configurations. We aimed to determine whether significant computational efficiencies were possible by adopting a streamlined approach, provided that the risk assessment distributions demonstrated comparability between the conventional and reduced methodologies. Through this analysis, we proved the effectiveness of leveraging specific features such as location and time to improve the computation of privacy risk assessment in Foursquare-based trajectory data. Table 9 provides \(p\)-values for attacks using location values with lower entropy at a \(k\) value of 1. All \(p\)-values indicate no statistically significant differences, with values of 1 for all attack types. In both cases, location and time, \(p\)-values are 1 for all percentages, indicating no significant variations in the risk distribution. The same observation can be seen with statistics values in Table 10. All values are zero, which means that the distributions are the same. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Feature** & **Attack** & **k** & \multicolumn{6}{c}{**Low-Entropy Percentile (\%)**} \\  & & & **Original** & **10** & **20** & **30** & **40** & **50** \\ \hline
**Location** & Visit & 1 & 7 d 12:23:57 & 0 d 23:37:37 & 1 d 17:29:53 & 2 d 12:13:42 & 3 d 05:19:08 & 3 d 21:41:34 \\
**Location** & Visit & 2 & 69 d 21:08:34 \({}^{*}\) & 16 d 08:16:34 & 27 d 23:14:20 & 38 d 13:14:57 & 47 d 05:13:02 & 54 d 04:18:26 \({}^{*}\) \\
**Time** & Visit & 1 & 7 d 12:24:46 & 0 d 23:37:46 & 1 d 17:30:03 & 2 d 12:15:36 & 3 d 05:19:26 & 3 d 21:41:34 \\
**Time** & Visit & 2 & 69 d 21:08:35 \({}^{*}\) & 16 d 08:16:35 & 27 d 23:14:23 & 38 d 13:14:47 & 47 d 05:16:15 & 54 d 04:18:20 \({}^{*}\) \\
**Location** & Location Sequence & 1 & 7 d 12:23:57 & 0 d 23:37:36 & 1 d 17:29:50 & 2 d 12:13:44 & 3 d 05:20:17 & 3 d 21:41:26 \\
**Location** & Location Sequence & 2 & 69 d 21:08:22 \({}^{*}\) & 16 d 08:15:24 & 27 d 23:13:08 & 38 d 13:14:22 & 47 d 05:13:11 & 54 d 04:18:45 \({}^{*}\) \\ \hline \hline \end{tabular} d = days, \({}^{*}\) = estimated value.  
\end{table} 
Table 7: Breadcrumbs dataset: comparing execution time of the **Original** with the **Low-Entropy Percentile** approach. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Feature** & **Attack** & **k** & \multicolumn{6}{c}{**Low-Entropy Percentile (\%)**} \\  & & & **Break** & **10** & **20** & **30** & **40** & **50** \\ \hline
**Location** & Visit & 1 & 1 d 20:14:54 & 13:54:21 & 13:54:30 & 13:55:27 & 13:56:30 & 13:57:22 \\
**Location** & Visit & 2 & 1 d 11:27:51 & 32:54:00 & 32:55:22 & 32:56:11 & 32:57:17 & 32:58:00 \\
**Time** & Visit & 1 & 13:45:33 & 0:01:421 & 0:01:43 & 00:15:11 & 00:15:34 & 00:15:54 \\
**Time** & Visit & 2 & 13:52:53 & 00:37:22 & 00:38:11 & 00:39:31 & 00:39:33 & 00:39:41 \\
**Location** & Location sequence & 1 & 1 d 20:14:54 & 00:40:35 & 00:41:05 & 00:41:48 & 00:42:30 & 00:43:15 \\
**Location** & Location Sequence & 2 & 1 d 11:27:51 & 09:45:00 & 09:46:12 & 09:47:09 & 09:48:24 & 09:49:23 \\ \hline \hline \end{tabular} d = days.  
\end{table} 
Table 8: Breadcrumbs dataset: comparing execution time of **Break** with **Break** and **Low-Entropy Percentile**. The successful performance of the time- and location-reduced set approach in the Foursquare, as can be seen in Figure 6, and Breadcrumb, as shown in Figure 5, datasets can be attributed to the high uniqueness in both dimensions. These datasets likely exhibit diverse location and time values, making them suitable for re-identification risk computation mitigation strategies. The effectiveness of this method improves as the \(k\) size increases. Increasing the granularity (larger \(k\)) for datasets with less unique information can enhance the quality of the re-identification risk computation mitigation result.