## 3 Proposed Model
### Feature Extraction
#### 3.4.2 Kinematic Features  
In our experiment, for better classification, 10 different kinematic features are extracted as shown in Table 3. The \(X\)-axis value has been measured by the difference of the \(X\)-axis's value by different variations of the period. We measured the \(x\)-axis velocity (horizontal velocity) by subtracting the \(x\)-axis's value of \(X_{n}\) from that of \(X_{n-1}\). The mathematical formula of \(X\)-axis velocity is:  
\[Horizontal\ velocity=\sum_{n=1}^{N}\frac{x_{n+1}-x_{n}}{t_{n+1}-t_{n}} \tag{1}\]  
where, \(N\) represents the length of the input data of each person, \(t_{n}\) is the elapsed time after the start of the test, \(P_{n}\) is the writing pressure, \(X_{n}\) is the positional coordinate in the horizontal direction, and \(Y_{n}\) is the positional coordinate in the vertical direction. The \(Y\)-axis velocity (vertical velocity) has been measured from its \(Y\)-axis value difference with its time variation at each iteration. The average velocity has been located using the length and square root of the velocity of the \(X\)-axis and \(Y\)-axis. The mean pressure has been calculated through the mean of writing pressure. The peak pressure has been calculated from the highest pressure which is greater than the mean pressure. The peak pressure is different from person to person.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Features** & **Equation** & **Features** & **Equation** \\ \hline Average Pressure & P\({}_{\text{ram}}=\frac{1}{N}\sum\limits_{n=1}^{N}\left(\text{P}_{n}\right)\) & Peak Pressure & P\({}_{\text{peak}}=1\leq n\leq\text{Nmax}\left(\text{P}_{n}\right)\) \\ \hline Average Velocity & V\({}_{\text{mean}}=\frac{\sqrt{\left(\text{P}_{n}-\text{N}_{n+1}\right)^{2}}+ \left\{Y_{n}-\text{P}_{n+1}\right\}^{2}}{\left(\text{P}_{n+1}-\text{P}_{n} \right)}\) & Peak Velocity & V\({}_{\text{max}}-\text{max}_{1\leq n\leq N}\frac{\sqrt{\left(\text{P}_{n}-\text{N}_{n+1} \right)^{2}}+\left\{Y_{n}-\text{P}_{n+1}\right\}^{2}}{\left(\text{P}_{n+1}- \text{P}_{n}\right)}\) \\ \hline Average Start Position of Pen & P\({}_{\text{start}}-\text{N}*\frac{1}{0.05}\sum\limits_{n=1}^{N+0.05}\text{P}_{n}\) & Average End Position of Pen & P\({}_{\text{End}}-\text{N}*\frac{1}{0.05}\sum\limits_{n=1}^{N+0.95}\text{P}_{n}\) \\ \hline Average Writing Start & \(\underset{\text{Velocity}}{\text{Average Writing End}}\) & \(\underset{\text{Velocity}}{\text{Velocity}}\) & \(\underset{\text{Velocity}}{\text{Velocity}}\) & \(\underset{\text{Velocity}}{\text{Velocity}}\) \\ \hline Horizontal Velocity & V\({}_{\text{h}}=\sum\limits_{n=1}^{N}\frac{\text{P}_{n+1}-\text{P}_{n}}{\text{P}_{n+1}- \text{P}_{n}}\) & Vertical Velocity & V\({}_{\text{v}}=\sum\limits_{n=1}^{N}\frac{\text{P}_{n+1}-\text{P}_{n}}{\text{P}_{n+1}- \text{P}_{n}}\) \\ \hline \end{tabular}
\end{table}
Table 3: Kinematic Features from Sensor Data.  
Writing Velocity is the rate of change of the position of the pen tip over time. The writing velocity has been measured from horizontal direction and vertical direction. The average start position is the rate of change of the start position of the pen tip over time. The average end position is the rate of change of the end position of the pen tip over time. The horizontal velocity and vertical velocity of each person are not changing much i.e., it also remains constant for each individual.