## 5 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Model** & **Feature** & **E1** & **E2** & **E3** & **E4** & **E5** & **F1** & **F2** & **F3** & **F4** & **F5** & **K1** & **K2** & **K3** \\ \hline TCN & Coordinate-A & **0.997** & **0.997** & **0.997** & **0.990** & **0.995** & **0.989** & **0.992** & **0.986** & **0.990** & **0.990** & **0.996** & **0.990** & **0.996** & 0.990 \\  & & **(0.005)** & **0.013** & **0.010** & **0.022** & **0.019** & **0.011** & **0.024** & **0.012** & **0.027** & **0.014** & **0.022** & **0.009** & **0.009** & (0.020) \\ RNN & Coordinate-B & 0.977 & 0.982 & 0.977 & 0.970 & 0.978 & 0.972 & 0.971 & 0.978 & 0.963 & 0.958 & 0.963 & 0.968 & 0.975 \\  & & 0.034 & (0.025) & (0.029) & (0.036) & (0.039) & (0.027) & (0.034) & (0.025) & (0.039) & (0.049) & (0.044) & (0.035) & (0.034) \\ RNN & Full & 0.988 & 0.982 & 0.986 & 0.980 & 0.974 & 0.967 & 0.959 & 0.972 & 0.966 & 0.960 & 0.980 & 0.990 & **0.990** \\  & & (0.026) & (0.030) & (0.028) & (0.034) & (0.054) & (0.047) & (0.070) & (0.040) & (0.052) & (0.055) & (0.040) & (0.023) & **0.018** \\ RNN & Angular-A & 0.981 & 0.956 & 0.980 & 0.960 & 0.951 & 0.943 & 0.946 & 0.956 & 0.946 & 0.941 & 0.974 & 0.974 & 0.982 \\  & & (0.041) & (0.090) & (0.037) & (0.065) & (0.093) & (0.083) & (0.091) & (0.063) & (0.087) & (0.076) & (0.049) & (0.050) & (0.036) \\ RNN & Angular-B & 0.956 & 0.934 & 0.949 & 0.938 & 0.915 & 0.919 & 0.901 & 0.934 & 0.910 & 0.896 & 0.941 & 0.952 & 0.961 \\  & & (0.087) & (0.139) & (0.083) & (0.077) & (0.155) & (0.111) & (0.163) & (0.063) & (0.133) & (0.111) & (0.135) & (0.130) & (0.091) \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Average AUROC result obtained by the TCN model. Numbers in parentheses denote standard deviation and the text in bold denotes the best performance for each drawing pattern. E, F, and K denote English, freestyle, and Korean patterns, respectively. The average AUROC for the TCN- and RNN-based models according to the lengths of the used 13 patterns and for the 5 combinations of the variable sets are depicted in Figures 11 and 12, respectively. It can be observed that for both TCN and RNN, the authentication performance of the angular feature-based models (Angular-A and Angular-B) deteriorates when the pattern length increases. In contrast, the coordinate-based models were relatively less affected by this trend. This is because the gyroscope in the smartphone that measured the angular velocity is relatively less precise that the touch sensor that captured the coordinate features. Hence, angular-based features were more likely to be affected by the noise when the sequence length increased. Among them, the Coordinate-A-based model exhibits the best user-authentication performance and the best robustness to pattern length in comparison with other variable combination sets. The training and inference time consumption while using Coordinate-A-based TCN and RNN models are presented in Tables 16 and 17, respectively. The main difference between these two models is that TCN conducts convolutional operations simultaneously but RNN conducts the LSTM operation sequentially. Therefore, when longer sequential data are used, RNN required considerably more time than TCN to process the entire data. Therefore, in all experimental cases, both the training and inference times for TCN are relatively smaller than those for RNN. Based on the experimental results, the minimum and maximum values of the ratio of RNN's consumption of training time to that of TCN are  
Figure 11: Average AUROC according to sequence length for each variable combination set by TCN (x-axis: sequence length, y-axis: AUROC).