## 6 Experiments
### Selecting Background Knowledge Configurations with Low-Entropy Feature Frequency
#### 6.5.2 Breadcrumbs  
Now, we present the analysis of the Breadcrumbs dataset. Our objective was to examine the distribution of re-identification risk and explore the potential implications of targeting low entropy and feature frequency within background knowledge configurations. We aim to verify whether real computational benefits are achievable by adopting our low-entropy approach, demonstrating that the risk assessment distributions exhibit similarity \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Feature**} & \multirow{2}{*}{**Attack**} & \multirow{2}{*}{**k**} & \multicolumn{6}{c}{**Break** and **Low-Entropy Percentile**} \\  & & & & **Break** & **10** & **20** & **30** & **40** & **50** \\ \hline
**Location** & Visit & 1 & 141 d 14:00:20 * & 117 d 21:35:56 * & 122 d 06:13:04 * & 126 d 04:03:50 * & 129 d 21:23:35 * & 132 d 05:01:04 * \\
**Location** & Visit & 2 & 420 d 11:00:30 * & 261 d 18:08:00 * & 299 d 04:57:55 * & 330 d 22:00:50 * & 356 d 05:17:00 * & 357 d 10:04:31 * \\
**Time** & Visit & 1 & 141 d 09:28:44 * & 116 d 19:04:06 * & 120 d 25:27:17 * & 124 d 18:03:17 * & 128 d 10:43:16 * & 131 d 03:22:09 * \\
**Time** & Visit & 2 & 460 d 15:01:30 * & 276 d 10:08:00 * & 318 d 01:42:22 * & 354 d 01:34:19 * & 375 d 17:59:05 * & 393 d 17:07:11 * \\
**Location** & Location Sequence & 1 & 20 d 09:03:30 * & 3 d 01:13:30 & 5 d 03:45:08 & 7 d 06:02:21 & 9 d 05:41:11 & 11 d 02:18:06 \\
**Location** & Location Sequence & 2 & 224 d 04:56:55 * & 697 d 25:27:17 * & 1038 d 00:35:24 * & 132 d 15:14:34 * & 1593 d 03:25:48 * & 1787 d 20:57:34 \\ \hline \hline \end{tabular} d = days, * = estimated value.  
\end{table} 
Table 4: Wi-Fi dataset: comparing execution time of **Break** with **Break** and **Low-Entropy Percentile**. Figure 4: Comparison of uniqueness of each feature in Wi-Fi dataset. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Feature**} & \multirow{2}{*}{**Attack**} & \multirow{2}{*}{**k**} & \multicolumn{6}{c}{**Low-Entropy Percentile (\%)**} \\  & & & **Original** & **10** & **20** & **30** & **40** & **50** \\ \hline
**Location** & Visit & 1 & 2314 d 15:56:33 * & 333 d 18:45:46 * & 578 d 14:04:24 * & 823 d 06:47:46 * & 1027 d 18:24:01 * & 1265 d 06:34:33 * \\
**Location** & Visit & 2 & 60,396 d 10:50:50 * & 16,147 d 14:04:09 * & 26,568 d 23:45:23 * & 35,472 d 21:27:27 * & 24,547 d 12:22:11 * & 48,221 d 10:50:22 * \\
**Time** & Visit & 1 & 220 d 11:28:24 * & 279 d 14:02:02 * & 506 d 13:32:52 * & 7,43 d 07:43:6 * & 97 d 18:24:16 * & 1138 d 06:13:00 \\
**Location** & Visit & 2 & 66,150 d 12:34:55 * & 14,333 d 11:20:50 * & 25,97 d 18:57:24 * & 35,380 d 01:18:53 * & 43,744 d 12:00 * * & 50,564 d 22:33:6* \\
**Location** & Location Sequence & 1 & 20 d 21:03:00 * & 3 d 00:10:10 * & 5 d 04:66:02 & 7 d 09:07:40 * & 9 d 108:58:54 & 11 d 03:03:32 \\
**Location** & Location Sequence & 2 & 9793 d 01:38:34 * & 2622 d 15:25 * & 4315 d 06:34:55 * & 576 d 05:53:01 * & 691 d 02:56:44 * & 7824 d 13:56:32 * \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Wi-Fi dataset: comparing execution time of the **Original** with the **Low-Entropy Percentile** approach. between the conventional and reduced methodologies. This analysis shows the efficacy of leveraging specific features such as location and time to support privacy risk assessment in breadcrumb trajectory data. Table 5 presents \(p\)-values for various attacks using location and time-frequency with lower entropy to reduce the background knowledge set compared with the standard approach and considering different \(k\) sizes. The \(p\)-values, all equal to 1, indicate no statistically significant differences in the distribution of re-identification risk across different k sizes. It implies that the location and time features are sufficiently unique, as seen in Figure 5, to serve as filters for selecting background knowledge configurations prone to having maximum risk. The same observation can be seen with statistics values in Table 6. All values are zero, which means that the distributions are the same.