## 4 Experimental Results
### Performance Evaluation  
The performance assessment of the three implemented ML models--KNN, RF, and GBM--with and without incorporating TOPSIS methodology-based feature ranking is elucidated in Table 2. Based on the experimental results, it is pointed out that the KNN model performed well on small datasets; however, it encountered a problem with scalability when the data size was significantly elevated. The GBM model accomplished high accuracy due to its iterative boosting process, yet it needed longer training time. RF model offered a good solution balance between computational efficiency and accuracy, and this renders the system more appropriate for real-time applications and processing systems. Note that the RF model produced the highest accuracy compared to the two other models, KNN and GBM. Also, it was pointed out that classification accuracy was refined when TOPSIS-methodology-based feature chosen ranking was augmented, and this further emphasized that the feature selection approach was valuable. A good balance between computational efficiency and performance could be obtained based on this comparative assessment leveraging the most suitable model for authentication system purposes. To further clarify the efficiency of this trade-off, it was observed that the application of TOPSIS improved training efficiency by reducing the input feature set, which, in turn, lowered the overall computational complexity during model training. This supports the use of feature ranking in real-time mobile authentication, where reducing computational latency is a critical requirement. Although TOPSIS introduces an additional preprocessing step, it helps reduce the input dimensionality by eliminating less relevant features before classification. This dimensionality reduction led to faster training and inference processes, as the classifiers operated on fewer inputs. While no exhaustive benchmarking was conducted, the observed improvement in training efficiency and resource usage supports the suitability of this method for real-time mobile environments.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **TOPSIS Score** & **Rank** \\ \hline Touch pressure & 0.5053 & 1 \\ X-coordinate & 0.4602 & 2 \\ Velocity & 0.4562 & 3 \\ Y-coordinate & 0.4353 & 4 \\ \hline \hline \end{tabular} Note: All models were tested on the same dataset collected in this study using consistent settings.  
\end{table}
Table 1: Performance comparison of classifiers with and without TOPSIS on the same dataset.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**RF**} & \multicolumn{2}{c}{**GBM**} & \multicolumn{2}{c}{**KNN**} \\ \cline{2-7}
**Metric** & **Without** & **With** & **Without** & **With** & **Without** & **With** \\  & **TOPSIS** & **TOPSIS** & **TOPSIS** & **TOPSIS** & **TOPSIS** & **TOPSIS** \\ \hline Accuracy & 90.4\% & 94.8\% & 90.13\% & 94.7\% & 83.42\% & 93.8\% \\ Precision & 88.9\% & 94.8\% & 91.09\% & 94.3\% & 81.24\% & 93.5\% \\ Recall & 90.89\% & 95.5\% & 89.78\% & 94.9\% & 83.31\% & 94.1\% \\ F1-Score & 90.15\% & 95.1\% & 89.35\% & 94.6\% & 81.37\% & 93.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance metrics of the proposed models.  
The comparative results shown in Table 2 reflect the influence of applying TOPSIS-based feature ranking before classification. All three classifiers demonstrated improved performance metrics when trained on the reduced feature set selected by TOPSIS. This suggests that TOPSIS effectively filtered out less informative or redundant features, leading to sharper class boundaries and reduced model variance. While a formal decision-boundary visualization is beyond the current scope, the observed increase in precision and F1-Score indicates enhanced separability between genuine and impostor interactions.