# Process Mining IPTV Customer Eye Gaze Movement Using Discrete-Time Markov Chains +
## 4 Results
### DTMC-\"Content Purchase\" Screens
#### 4.1.1 Transition Matrix-Screen A&B  
The transition matrix for the initial states A-F for screen A, as well as including the non-AOI (Z) and \"Payment\" states, have been generated. This allows the expected number of steps and time to absorb into the \"Payment\" state to be calculated afterwards. The directed graph, which is the visualisation of the DTMC in MATLAB, has also been created. Figure 12(a),b, respectively, show the transition matrix and plotting for the DTMC model of screen A. In terms of the transition matrix in Figure 13a, the highest probabilities fall along the diagonal, suggesting that the most frequent state change is to remain within that state for the next period, which makes sense for this data as the timestamps are recorded every 00:00:00.165 s and if the user is focusing on an image or reading some text then this will require a greater period than jumping from fixating on one AOI to the next. In both Figure 13a,b, state A is accessible from state D, but this is not the case vice-versa, as state D is not directly accessible from state A. In terms of AOIs, this suggests that the viewer's eye trajectories can begin at \"Buy to own SD\" and return to the \"Packshot image,\" but never from the \"Packshot\" to the \"Buy to own SD\" button. This would further suggest that viewers either glance directly to the right from the \"Packshot\" to the information or straight down to the \"Buy to own HD\" button. This could potentially be due to the \"Buy to own HD\" button being highlighted in a different colour than the rest of the buttons, therefore drawing the viewers' eyes immediately. Similarly, the transition matrix and directed graph for screen B are shown in Figure 14a,b below. It can be seen that the same pattern is emerging as with screen A, albeit with fewer states available. It is interesting that despite being a different screen, the users never directly access from state A to D, only D to A, suggesting the \"Buy SD\" option does not immediately draw their interest from the \"Packshot\", and instead, the user fixates on the information or the \"Buy HD\" option after looking at the Packshot image. This agrees with the concept that we observe computer screens horizontally and vertically, in a traditional \"F\" shape, much more frequently than diagonally. Once again, in the transition matrix for Screen B in Figure 14a, the highest transitional probabilities are along the diagonal, where the fixations remain within the same state for a prolonged period. For both screens, the non-AOI (Z) state communicates with all states as it covers a large area surrounding all of the AOIs. For screen A, the \"Payment\" state can be accessed from both state C and the non-AOI state, while for screen B, the \"Payment\" state is accessible from states C and D and the non-AOI state(Z). This could be a result of users reading the \"Buy or Rent?\" information at the bottom of the page before proceeding to payment. The bottom row of each matrix shows the Payment state is absorbing, with all of the probabilities of the payment state reaching a different state equal to 0, while the probability of remaining within the payment state once it has been entered is equal to 1. As this is an absorbing state and as Figures 13 and 14 represent an accurate model of each screen, now the expected time to absorption (Payment) can be calculated. Figure 13: (a) Transition Matrix for Screen A; (b) DTMC Plot for Screen A. From the perspective of HCI analysis, for both screens A and B, state C is the 'Buy to Own HD button', which is on the left-hand side and highlighted in a pale grey colour which heavily contrasts against the dark grey background, while the other buttons appear in a much darker purple colour that is less of a contrast against the black background. As the button is on the left-hand side, the user's eyes will naturally be drawn more to it than the buttons on the right-hand side.