## 5 Simulation and Results  
### Computational Time Comparison  
As depicted in Figure 21, in all four algorithms, there was a significant decrease in the computational time required after applying area division, although each algorithm showed distinct levels of improvement. To compare them with each other, the specific parameters of each algorithm were first optimized. After finding the optimal parameters, the execution time for each method was calculated. The total execution time includes the time spent on the data classification process (for area division) and the location prediction process. In Figure 21, the red column shows the total CPU time before area division, while the orange and yellow columns show the total execution time for unseen data that belong to the edge area and the center area, respectively, after area division. An unknown data can only belong to either the center area or the edge area. Once this data is in the center area, the total CPU time will not include the location estimation time for the edge area data, and vice versa. Table 3 presents the exact time of each method, while the level of improvement in CPU time for each proposed algorithm is shown in Table 4.  
Figure 19: Mean score vs. number of trees.  
Figure 20: Mean and standard deviation of positioning errors vs. number of trees by: (**a**) whole floor, (**b**) center area, and (**c**) edge area.  
It is clear that the system with SVM suffers from the heaviest computation burden but also presents the greatest improvement in execution time after area division. The improvement was 86.21% for the center area and 70.31% for the edge area (see Table 4). The kNN and DT algorithms execute much faster than RF and SVM, with total times of 7.5 ms, and 7.19 ms, respectively. Furthermore, unlike SVM, the time improvement in DT is the lowest of the four suggested methods, with 10.85% for the center area and 70.31% for the edge area.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Position of Data** & **SVM** & **RF** & **kNN** & **DT** \\ \hline
**Center** & 86.21 & 32.29 & 29.47 & 10.85 \\
**Edge** & 70.31 & 26.04 & 21.47 & 6.40 \\
**Average** & 78.26 & 29.17 & 25.47 & 9.63 \\ \hline \hline \end{tabular}
\end{table}
Table 4: CPU time level of improvement after area division (%).  
Figure 21: Computational time comparison before and after area division.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **Position of Data** & \
\begin{tabular}{c} **Area Division** \\ **Time** \\ \end{tabular} &
\begin{tabular}{c} **Location** \\ **Prediction Time** \\ \end{tabular} & **TOTAL TIME** \\ \hline \multirow{3}{*}{**SVM**} & Whole floor & No classification & 195.00 & 195.00 \\  & Center Area & 6.90 & 20.00 & 26.90 \\  & Edge Area & 6.90 & 51.00 & 57.90 \\ \hline \multirow{3}{*}{**RF**} & Whole floor & No classification & 96.00 & 96.00 \\  & Center Area & 11.00 & 54.00 & 65.00 \\  & Edge Area & 11.00 & 60.00 & 71.00 \\ \hline \multirow{3}{*}{**kNN**} & Whole floor & No classification & 7.50 & 7.50 \\  & Center Area & 0.59 & 4.70 & 5.29 \\  & Edge Area & 0.59 & 5.30 & 5.89 \\ \hline \multirow{3}{*}{**DT**} & Whole floor & No classification & 7.19 & 7.19 \\  & Center Area & 1.10 & 5.31 & 6.41 \\ \cline{1-1}  & Edge Area & 1.10 & 5.63 & 6.73 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Computational time (ms).  
the center area and 6.4% for the edge area. In summary, all four methods show a significant reduction in computation cost after area division is performed using classification.