# Comparative Analysis of Major Machine-Learning-Based Path Loss Models for Enclosed Indoor Channels
## 5 Results and Discussions
Finally, the predicted and actual path loss values are given in Figure 8. Again, the figure proves what we have discussed in this section: all the models have a significant prediction performance with the best accuracy provided by all the models since there are clear straight lines, except the MLR model with an inaccurate performance. The validation and training loss in Figure 9 shows the excellent fitting of the ANN and RNN models since the validation curve is slightly higher than the testing curve in the case of the ANN model, while the validation curve matches the testing curve across all the epoch values in the case of the RNN-LMTS model. The results reveal that the structure of these neural networks provides high precision in fitting the measurement data without underfitting or overfitting issues. Figure 10 depicts the measured and predicted path loss and the prediction error of all the ML-based models selected in this work. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline
**Models** & \multicolumn{3}{c}{\(\mathbf{R^{2}}\)} & \multicolumn{3}{c}{**RMSE**} & \multicolumn{3}{c}{**MAPE**} & \multicolumn{3}{c}{**MSE**} & \multicolumn{3}{c}{**Corr**} \\ \hline  & **Min** & **Avg** & **Max** & **Min** & **Avg** & **Max** & **Min** & **Avg** & **Max** & **Min** & **Avg** & **Max** & **Min** & **Avg** & **Max** \\ \hline MLR & 0.4704 & 0.5220 & 0.5711 & 2.5191 & 2.7713 & 2.9008 & 0.0220 & 0.0239 & 0.0252 & 6.3461 & 7.6943 & 8.4144 & 0.6945 & 0.7274 & 0.7573 \\ PMR & 0.8743 & 0.9286 & 0.9556 & 0.8721 & 1.0480 & 1.2856 & 0.0059 & 0.0072 & 0.0087 & 0.7605 & 1.1248 & 1.6528 & 0.9550 & 0.9679 & 0.9781 \\ SVR & 0.9054 & 0.9414 & 0.9798 & 0.5369 & 0.9252 & 1.1586 & 0.0037 & 0.0054 & 0.0064 & 0.2882 & 0.8952 & 1.3423 & 0.9520 & 0.9731 & 0.9907 \\ DT & 0.8690 & 0.9125 & 0.9473 & 0.8678 & 1.1653 & 1.5263 & 0.0052 & 0.0068 & 0.0085 & 0.7531 & 1.3988 & 2.3296 & 0.9342 & 0.9606 & 0.9743 \\ RF & 0.9189 & 0.9461 & 0.9688 & 0.6680 & 0.9145 & 1.2534 & 0.0041 & 0.0055 & 0.0070 & 0.4463 & 0.8688 & 1.5709 & 0.9696 & 0.9983 \\ KNN & 0.9068 & 0.9443 & 0.9756 & 0.5909 & 0.9175 & 1.2163 & 0.0040 & 0.0052 & 0.0058 & 0.3492 & 0.8787 & 1.4794 & 0.9524 & 0.9747 & 0.9877 \\ ANN & 0.9017 & 0.9352 & 0.9755 & 0.0270 & 0.0355 & 0.0435 & 0.0220 & 0.0312 & 0.0587 & 0.0007 & 0.0013 & 0.0019 & 0.9530 & 0.9732 & 0.9878 \\ RNN-LSTM & 0.8889 & 0.9160 & 0.9762 & 0.0216 & 0.0418 & 0.0592 & 0.0161 & 0.0390 & 0.0694 & 0.0005 & 0.0019 & 0.0035 & 0.9433 & 0.9666 & 0.9882 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance metrics’ values of all the ML-based models selected. Runtime analyses of ML models are essential for understanding the complexity of machine learning algorithms. It is crucial for algorithm selection in specific tasks and vital for successful implementation. Therefore, it is always a good practice to do runtime analysis and comprehend the complexity of ML algorithms. Runtime analysis can be seen from two directions: time complexity and space complexity. Time complexity measures how fast or slow a model performs the task, while space complexity is the amount of memory required to execute the task. In this work, time complexity analysis is performed to study the comparison between the adopted ML models. Table 2 represents the runtime of each model where some models take less than a second to complete the task, such as MLR, PL, DT, and KNN, while others take more time to finish the task. More specifically, as depicted in Table 2, the minimum runtime was achieved by the MLR model, 21.3 ms, which means that the MLR model has the least complexity among the other models. Nevertheless, the MLR model has the worst performance according to the results presented in Table 1. The highest runtime was observed from the run of the RNN-LSTM model since it took almost 125 s to train the model. In general, the runtime obtained by our ML models is comparatively short, which indicates that the adopted models can fit the path loss problems with relatively low complexity.