## 4 ReMouse Dataset Analysis  
### Sessions Generated by The Same User  
In the first stage of our ReMouse dataset study, we focused on analyzing the sessions generated by each individual user in isolation from other users. For the purpose of this analysis, a mouse cursor trajectory of a particular session was modeled by means of two time-dependent variables: (1) 2D coordinates/position of the mouse cursor; (2) speed of mouse cursor. As an illustration, Figure 4 displays the trajectories comprising only the mouse coordinates (i.e., positional information) of session number 3 for ReMouse users 90 to 98. Figure 3: Session status. Figure 2: The number of sessions generated by each user. Our analysis of single-user sessions led to some interesting observations:  
**Observation 1.1**: It is evident from the collected data that by repeating the same online task over time (i.e., repeating multiple rounds of our 'Catch Me If You Can!' game), each user generally becomes faster and able to complete every subsequent round of the game in a progressively shorter amount of time. These findings are illustrated in Figure 5, which displays the 'time taken' and the 'average mouse movement speed' for user 82 (which is randomly chosen among the 100 participants) across each of the 16 rounds/sessions of the game that this particular user has performed. The same observation is also evident from Figure 6, which shows the dynamic time warping (DTW) distances [35] between the trajectories of subsequent pairs of sessions generated by user 82 (e.g., trajectories of first and second session, second and third session, etc.). As can be seen in Figure 6, the DTW distances between the trajectories of subsequent sessions become closer and shorter as the user keeps repeating the same task. Note that we opted for the use of the DTW distance metric in our analysis as it has allowed us to measure the distance between two sessions (two time series) of different lengths and different time-wise alignments (DTW re-aligns two feature vector sequences by warping the time axis iteratively until an optimal match between the two sequences is found [35]). Figure 7 provides a closer look into the trajectories of two particular sessions (number 13 and 14) of user 82 and their respective DTW cumulative distance. Figure 4: Visual representation of mouse cursor trajectory in the session with order number 3 for users 90 to 98. Figure 5: (**a**) Time taken to complete each of 16 conducted sessions for user number 82; (**b**) Average mouse movement speed for each of 16 conducted sessions. Figure 6: Cumulative difference/distance between subsequent pairs of sessions generated by user 82. Figure 7: (**a**) Trajectories of sessions 13 and 14 of user 82; (**b**) Cumulative DTW distance between two sessions. To confirm Observation 1.1, we also deployed simple 'trend line analysis' [36] on the ReMouse dataset. A trend line is a bounding line that captures a trend and rallying patterns in a given dataset. If the slope of the line is a positive value, it indicates the trend is increasing, and a negative value implies that the trend is decreasing. We employed this analysis to discover the trend in 'time taken to complete a session' and 'average mouse speed' in relation to the session order number for each participating user. The average value of the slope in 'time taken to complete a session' trend lines, when calculated across all the users, was 417.0, which is a good indication that with every subsequent session/repetition the users generally spent less time completing the task. On the other hand, the average value of the slope in the'speed of mouse movement' trend lines, when calculated across all users, was 10.0, which is further proof that users generally became faster in completing a similar online task with every subsequent session/repetition.