## 3 Classifier Training and Results
### Results for Datasets Consisting of the Parametrised IMU Signals  
For the parametrized signals (the \(SP\) training procedure), the classifier performances were evaluated for different time window widths \(T\) for which the statistical parameters of the signals were \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Decision** & **Cropped** & **Random** & **Cropped** & \multirow{2}{*}{\(k\)**-NN for**} & **SVM with** & **SVM with** \\  & **Tree** & **Decision** & **Forest** & **Forest** & & **RBF Kernel** & **3 rd Degree** \\ \hline
1. & 97.63 & 97.84 & 98.57 & 98.52 & 95.40 & 97.82 & 98.14 \\
2. & 97.58 & 97.79 & 98.56 & 98.55 & 95.57 & 97.80 & 98.22 \\
3. & 97.50 & 97.74 & 98.64 & 98.58 & 95.51 & 97.86 & 98.22 \\
4. & 97.66 & 97.88 & 98.62 & 98.55 & 95.55 & 97.76 & 98.08 \\
5. & 97.55 & 97.87 & 98.71 & 98.60 & 95.52 & 97.68 & 98.17 \\
6. & 97.45 & 97.86 & 98.56 & 98.52 & 95.41 & 97.79 & 98.10 \\
7. & 97.49 & 97.81 & 98.57 & 98.57 & 95.50 & 97.77 & 98.03 \\
8. & 97.52 & 98.01 & 98.64 & 98.61 & 95.64 & 97.88 & 98.23 \\
9. & 97.62 & 97.86 & 98.65 & 98.55 & 95.49 & 97.84 & 98.17 \\
10. & 97.85 & 98.04 & 98.79 & 98.78 & 95.45 & 97.87 & 98.23 \\ Mean \(\pm\) Std & 97.59 \(\pm\) 0.11 & 97.87 \(\pm\) 0.09 & 98.63 \(\pm\) 0.07 & 98.58 \(\pm\) 0.07 & 95.50 \(\pm\) 0.07 & 97.81 \(\pm\) 0.06 & 98.16 \(\pm\) 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of 10-fold cross-validation training—classification accuracy for the classifiers trained on the parametrized data consisting of 42 parameters (training procedure SP). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Decision** & **Cropped** & **Random** & **Cropped** & \multirow{2}{*}{\(k\)**-NN for**} & **SVM with** & **SVM with** \\  & **Tree** & **Decision** & **Forest** & **Random** & & **RF Kernel** & **3 rd Degree** \\  & **Tree** & **Tree** & **Forest** & & & **Polynomial** \\ \hline
1. & 97.45 & 97.59 & 98.17 & 98.05 & 98.19 & 94.27 & 92.58 \\
2. & 97.41 & 97.59 & 98.27 & 98.14 & 98.24 & 94.14 & 92.54 \\
3. & 97.48 & 97.57 & 98.26 & 98.13 & 98.21 & 94.31 & 92.59 \\
4. & 97.41 & 97.59 & 98.26 & 98.11 & 98.21 & 94.05 & 92.39 \\
5. & 97.41 & 97.52 & 98.18 & 98.06 & 98.20 & 94.25 & 92.53 \\
6. & 97.43 & 97.57 & 98.19 & 98.08 & 98.17 & 94.26 & 92.55 \\
7. & 97.45 & 97.60 & 98.27 & 98.10 & 98.19 & 94.28 & 92.53 \\
8. & 97.43 & 97.61 & 98.29 & 98.13 & 98.28 & 94.02 & 92.32 \\
9. & 97.42 & 97.63 & 98.23 & 98.11 & 98.22 & 94.14 & 92.41 \\
10. & 97.40 & 97.58 & 98.22 & 98.12 & 98.21 & 94.43 & 92.72 \\ Mean \(\pm\) Std & 97.43 \(\pm\) 0.02 & 97.59 \(\pm\) 0.03 & 98.23 \(\pm\) 0.04 & 98.11 \(\pm\) 0.03 & 98.21 \(\pm\) 0.03 & 94.22 \(\pm\) 0.12 & 92.51 \(\pm\) 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of 10-fold cross-validation training—classification accuracy for the classifiers trained on the IMU signal samples (training procedure \(TDR\)). calculated. The results obtained for the combined test scenarios \(T1\) and \(T2\) are shown in Figure 4 for different time window sizes. Also, Figure 5 compares the results of head gesture classifications obtained for two different testing datasets, i.e., the test data for trial participants whose data was used for training the classifiers and the test data from trial participant whose data was not used for training the classifiers. We can conclude that the results shown in Figure 5 show the user independent performance of the system. Interestingly (as illustrated in Figure 4), the best results were obtained for the shortest time window, i.e., \(T=0.1\) s window containing 10 signal samples. An increase in the width of the time window negatively affected the classification accuracy. Note that for the test dataset, regardless of the width of the time window, the best classifier was the SVM with a 3 rd degree polynomial kernel (accuracy better than 92%).