## 3 Data Collection: The Cyber Identity and Biometrics Lab: Mouse Dynamics Dataset
### Mouse Movement Action Features  
There are numerous movement-based features that can be harvested from a continuous time-series dataset: velocity of mouse pointer, acceleration, jerk, angle of movement, angular velocity, number of pixels travelled, curvature, and curvature change rate. Each feature is briefly described in the following sections. Velocity is the rate at which distance is changing per unit in a definite direction. Velocity along the \(x\)-axis, velocity along the \(y\)-axis, the magnitude of velocity over the mouse plane, and angular velocity were computed on the basis of \(x(t)\), \(y(t)\) and \(\Theta(t)\) series using the following Equations (1)-(4), respectively. \[v(x,t)=\frac{x(t)-x(t-1)}{t-(t-1)} \tag{1}\]  
\[v(y,t)=\frac{y(t)-y(t-1)}{t-(t-1)} \tag{2}\]  
\[v(pixels,t)=\sqrt{v(x,t)^{2}+v(y,t)^{2}} \tag{3}\]  
\[W=(\Delta^{\rightarrow}\theta/\Delta^{\rightarrow}t) \tag{4}\]  
In addition, acceleration is defined as change in velocity per unit time. Acceleration-based features are acceleration along the \(x\)-axis, acceleration along the \(y\)-axis, and magnitude of acceleration over the mouse plane, respectively, Equations (5)-(7). \[a(x,t)=\frac{v(x,t)-v(x,t-1)}{t-(t-1)} \tag{5}\]  
\[a(y,t)=\frac{v(y,t)-v(y,t-1)}{t-(t-1)} \tag{6}\]  
\[a(x,y,t)=a(pixels,t)=\sqrt{a(x,t)^{2}+a(y,t)^{2}} \tag{7}\]  
Another used feature was jerk. Jerk is defined as a change in acceleration per unit time. The jerk along the \(x\)-axis, jerk along the \(y\)-axis, and magnitude of acceleration over the mouse plan was computed using the following Equations (8)-(10):  
\[jerk(x,t)=\frac{a(x,t)-a(x,t-1)}{t-(t-1)} \tag{8}\]  
\[jerk(y,t)=\frac{a(y,t)-a(y,t-1)}{t-(t-1)} \tag{9}\]  
\[jerk(x,y,t)=\sqrt{jerk(x,t)^{2}+jerk(y,t)^{2}} \tag{10}\]  
Moreover, angular movement refers to direction of movement at a given timestamp. The **atan function(\(\Theta\))** using the \(x\) and \(y\) sequences was calculated. **Atan function(\(\Theta\))** is the angle of the path tangent with the \(x\)-axis. It can be calculated by the Equation (11) given below. \[v(y,t)=\frac{y(t)-y(t-1)}{t-(t-1)} \tag{2}\]0  
The **atan function** is a trigonometric function that is a common variation of the standard arctangent function; it can be used to define values related to a right triangle. Practically, the **atan** trigonometric function can be used to determine distances that are difficult to measure and produces results in the range \((-\pi,\pi)\) (Figure 7) [22]. In order to reduce the possible direction values, we used the 8 main directions defined by [PERSON] and [PERSON] (Figure 8) [1]. The speed(s) also was calculated for each action as the ratio of the travelled. Distance travelled refers to the number of pixels travelled within a second (Figure 7). It can be calculated by Equation (12). \[v(y,t)=\frac{y(t)-y(t-1)}{t-(t-1)} \tag{2}\]1  
Curvature distance is a ratio of distances in three consecutives recorded points on the screen. When a change in angular of the tangent per pixel divided by the length of the path from the origin point is found, the angle of curvature is computed (Figure 7). It can be calculated by the following Equation (13):  
\[v(y,t)=\frac{y(t)-y(t-1)}{t-(t-1)} \tag{2}\]2  
The curvature change rate was also calculated using Equation (14):  
\[v(y,t)=\frac{y(t)-y(t-1)}{t-(t-1)} \tag{2}\]3 The eight directions. Angles between \(0^{\circ}\) and \(45^{\circ}\) fall into the direction 1. \[v(y,t)=\frac{y(t)-y(t-1)}{t-(t-1)} \tag{2}\]4 Angular movement (\(\Theta\)), travelled distance, angle of curvature and its rate of change. \[v(y,t)=\frac{y(t)-y(t-1)}{t-(t-1)} \tag{2}\]5  
Curvature change rate refers to the change in curvature per pixel travelled divided by the length of the path from the origin point (Figure 8). Point-and-click features were extracted from mouse-based press actions and release actions. On the basis of press actions and release actions, we extracted two different datasets separately from the main dataset. The first extracted dataset contained only samples where the action is equal to \"PRESS\".