## 3 Proposed Model
### Parameters of Pen Tablet Handwriting Data  
In this research work, the dataset has six important parameters or attributes from which different kinematic and statistical features are calculated. The detailed explanations of these attributes are given below:  
1. _Writing Time:_ Every person consumes a different amount of time for his/her writing depending on the writing speed. Someone writes very slowly, someone writes moderately and someone writes very fast. After analysis, it is found that for those who write very fast, their handwriting style changes like their baseline changed over time such as rising, straight, falling, erratic, etc.
2. _Pen Pressure:_ Pen pressure is the most vital attribute of individual handwriting. Pen pressure of every individual is different from each other in terms of heavy or light. In our collected, dataset, the pressure of a person is not the same for each iteration. The pressure range of some person is (2345-6595) and some other person is (1978-22905).
3. _X-axis:_ The \(X\)-axis represents the writing position of a person from \(X\)-axis. We have taken a single keyword 5 times by the same person. It is noticed that the \(X\)-axis position value for each of the 5 cases is very close to each other which indicates that the \(X\)-axis value remains almost the same for each case for the same person. It ensures that the \(X\)-axis value is a promising attribute that can uniquely identify one person from another.
4. _Y-axis:_ The \(Y\)-axis indicates the writing position of a person from \(Y\)-axis. This position is different from each other. Like the \(X\)-axis position value, the \(Y\)-axis position value remains very similar in each iteration of the same person. The range of \(Y\)-axis value for some person is (1110-1201) and that of some other person has (1200-1350). Figure 3 shows \(x\)-axis and \(y\)-axis values for different persons for the same keyword.
5. _Horizontal Angle:_ The horizontal angle is the dimension of an angle within two lines, rising from the same spot. This angle is automatically measured by the pen tablet. To uniquely identify a user, the horizontal angle is one of the major attributes of our work. The maximum range of horizontal angles in the data set is below 500. Figure 4 shows that the horizontal angle remains constant over time.
6. _Vertical Angle:_ The vertical angels are the opposite angels to each other after passing two lines. This is also a major attribute of this research work to identify a user uniquely. In the data set, the maximum vertical angle is below 800. Figure 4 shows the horizontal and vertical angle of the same person which is kind of constant over time.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Time** & **Pressure** & **X-Axis** & **Y-Axis** & **Horizontal Angle** & **Vertical Angle** \\ \hline
6143.52 & 6787 & 346 & 1214 & 160 & 410 \\
6151.46 & 8707 & 346 & 1214 & 160 & 420 \\
6159.44 & 15,671 & 346 & 1214 & 161 & 420 \\
6166.47 & 15,847 & 346 & 1214 & 160 & 430 \\
6174.52 & 16,391 & 346 & 1214 & 161 & 430 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sample Dataset.  
Figure 4 represents how the writing angle (horizontal angle and vertical angle) of a person is changing over time. Writing angle is an attribute of the writer's handwritten data, this is not a model feature. From Figure 4, we can see that the horizontal and vertical angles of a person remain constant over time which can be considered as a vital attribute for a person. From here, we extracted some kinematic and statistical features such as horizontal velocity, vertical velocity, average writing start velocity, average writing end velocity, etc. Then those extracted features are used in our model. Therefore, there is no direct relation of this attribute (writing angle) with the model.  
Figure 4: Horizontal angle and vertical angle of the same person.  
Figure 3: Writing graph with the \(x\)-axis, \(y\)-axis values for different persons for the same keyword: (**a**) Person 1 (**b**) Person 2 (**c**) Person 3.