## 5 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Feature** & **E1** & **E2** & **E3** & **E4** & **E5** & **F1** & **F2** & **F3** & **F4** & **F5** & **K1** & **K2** & **K3** \\ \hline Coordinate-A & 0.60 & **0.03** & 0.23 & 0.22 & 0.07 & 0.80 & 0.39 & **0.00** & **0.05** & 0.30 & 0.46 & 0.59 & 0.07 \\ Coordinate-B & **0.00** & **0.00** & **0.00** & **0.05** & **0.00** & 0.06 & **0.01** & **0.00** & **0.00** & **0.00** & **0.00** & **0.00** & **0.02** \\ Full & **0.01** & **0.00** & **0.00** & **0.00** & **0.01** & **0.00** & **0.00** & **0.00** & **0.00** & **0.02** & **0.01** & **0.01** & **0.01** \\ Angular-A & 0.20 & **0.01** & 0.44 & **0.04** & 0.14 & **0.00** & **0.01** & 0.47 & **0.02** & 0.49 & 0.77 & 0.09 & 0.07 \\ Angular-B & 0.87 & 0.21 & 0.48 & 0.43 & **0.02** & 0.29 & **0.00** & 0.49 & **0.00** & 0.10 & **0.00** & **0.00** & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: \(p\)-value of one sided paired \(t\)-test of average AUROC of TCN and RNN models. Text in bold denotes \(p\)-value less than or equal to 0.05. E, F, and K denote English, freestyle, and Korean patterns, respectively. Figure 12: Average AUROC according to sequence length for each variable combination set by RNN (x-axis: sequence length, y-axis: AUROC). 4.66 and 11.89, respectively. Furthermore, the minimum and maximum values of the ratio of RNN's consumption of inference time to that of TCN are 5.25 and 12.66, respectively. The bubble plot in Figure 13 illustrates the time consumption for different patterns. It can be observed that the processing time based on the TCN structure is not significantly affected by the pattern length; however, that based on the RNN structure is highly dependent on the pattern length--the longer the pattern, the longer the processing time. This independence on the patten length of TCN can be a significant advantage when an authentication algorithm is implemented in an edge device with an insufficient computational capacity. Figure 14 illustrates the time consumption ratio of RNN to TCN with respect to the average sequence length of a pattern. It is clearly seen that the processing time for RNN rapidly increases in comparison with that of TCN; therefore, the ratio on the y-axis increases when the pattern length increases. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline  & **E1** & **E2** & **E3** & **E4** & **E5** & **F1** & **F2** & **F3** & **F4** & **F5** & **K1** & **K2** & **K3** \\ \hline Sequence length & 59.63 & 75.94 & 61.27 & 69.65 & 69.19 & 82.54 & 52.88 & 92.58 & 67.78 & 124.70 & 41.47 & 70.23 & 60.90 \\ TCN & 4.58 & 4.57 & 4.58 & 4.66 & 4.57 & 4.62 & 4.55 & 4.66 & 4.61 & 4.61 & 4.55 & 4.69 & 4.54 \\ RNN & 30.10 & 36.70 & 30.44 & 33.99 & 32.80 & 37.35 & 25.72 & 40.71 & 31.07 & 54.88 & 21.19 & 31.46 & 28.30 \\ Time ratio & 6.58 & 8.03 & 6.65 & 7.29 & 7.18 & 8.08 & 5.65 & 8.73 & 6.73 & 11.89 & 4.66 & 6.71 & 6.23 \\ RNN over TCN & & & & & & & & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 16: Time consumption during 300 iterations for training each algorithm based on Coordinate-A method (unit of time: seconds, batch size = 10, measurement by RTX 2080-Ti GPU). E, F, and K denote English, freestyle, and Korean patterns, respectively. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline  & **E1** & **E2** & **E3** & **E4** & **E5** & **F1** & **F2** & **F3** & **F4** & **F5** & **K1** & **K2** & **K3** \\ \hline Sequence length & 59.52 & 75.98 & 61.16 & 69.38 & 69.01 & 82.78 & 52.85 & 92.68 & 67.77 & 124.69 & 41.34 & 70.22 & 61.03 \\ TCN & 7.46 & 7.92 & 7.01 & 7.16 & 7.35 & 8.51 & 7.56 & 6.56 & 6.76 & 7.28 & 7.11 & 7.46 & 7.50 \\ RNN & 53.87 & 72.80 & 57.92 & 63.31 & 56.20 & 64.73 & 46.81 & 64.26 & 59.61 & 92.18 & 37.33 & 52.17 & 50.20 \\ Time ratio & 7.23 & 9.19 & 8.27 & 8.84 & 7.64 & 7.61 & 6.19 & 9.80 & 8.82 & 12.66 & 5.25 & 7.00 & 6.69 \\ RNN over TCN & & & & & & & & & & & & & & \\ \hline \end{tabular}
\end{table}