# Process Mining IPTV Customer Eye Gaze Movement Using Discrete-Time Markov Chains +
## 3 Methodology
### Fitting into a DTMC Model
#### 3.4.3 DTMC Modelling Steps  
In our study, to create a discrete-time Markov Chain (DTMC), there are three primary elements to define and calculate: (1) state space, (2) initial state probability distribution, and (3) transition matrix. 1. State space-AOI categories  
As mentioned before, Tobii Studio allows the user to define certain AOIs on the screen which are of more interest than others. In this case, for both \"content purchase\" and \"content viewing\" scenarios, we have divided the screen into several AOIs, represented \begin{table}
\begin{tabular}{l c} \hline \hline
**R Statement** & **Function Description** \\ \hline R \textgreater{} dtmc \textless{} new(”markovchain,” transitionMatrix = \(A\), states = \(L\)) & Create an object of the “markovchain” class, and, e.g., name it “dtmc” as an R variable \\ R \textgreater{} summary(dtmc) & Display properties and classification of states \\ R \textgreater{} communicatingClasses(dtmc) & Display communicating states \\ R \textgreater{} absorbingStates(dtmc) & Display absorbing states \\ R \textgreater{} steadyStates(dtmc) & Generate the steady-state vector (see Equation (9)) \\ R \textgreater{} meanFirstPassageTime(dtmc) & Create a matrix for the mean first passage times \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main functions available in “markovchain” R package. by rectangular blocks in Tobii Studio. For the Markov model about gaze movement, those AOIs are the states indicating where the gaze point falls during the Markov process. Similarly, in both scenarios, the onscreen area, apart from defined AOIs, is counted as a whole non-AOI part which is also considered a separate state in the Markov model. For the \"content purchase\" scenario, there are two possible screens: A and B. The AOIs for the two different types of screens available in the BT TV Player can be seen in Figure 4 below, with their AOIs defined as either A-F for screen A or A-D for screen B. Depending on the options available for the video content, screen A has 'Rent HD/SD' options in addition to 'Buy HD/SD', which is why there are more defined AOI E and F than screen B. For both screens, the letter Z has been assigned to the non-AOI sections of the screen. It refers to any area being fixated on the screen which does not include the AOIs A-F or A-D listed above. For example, if the TV viewer is reading the \"Buy\" or \"Buy or Rent?\" text information or fixating on the \"Cancel\" button, this is categorised as AOI 'Z'. For other common AOIs on both screens, A refers to the packshot image of the video, B shows a brief description, and C and D are the buying options for different definitions of quality. For the \"content viewing\" scenario, there is one screen in our study. Similarly, we have divided the screen into AOIs by content. The screenshot of all AOIs on the original screen can be seen in Figure 5 below. Also, to make it simple and clear, we have also made a layout-only screen based on all AOI blocks. Figure 4: “Content purchase”–Screen A & B (**A**: with rent option; **B**: without rent option). In Figure 5 above, block A has the BT TV logo, whereas blocks B through J include menu items. R features a large \"hero\" graphic for a programme being advertised. The K to N blocks provide additional information on this programme. S comprises shortcut buttons and overlaps R; hence, R is represented by two blocks. Both O and P display images and text as supplementary information. Q is positioned at the bottom of the page and provides a link to suggested shows. Block T refers to the area outside of the defined blocks, which is a non-AOI block. The next step is to convert the gaze movement data into transitions between AOIs so that we can apply DTMCs.