# Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics
## 4 The Backpack Process Model (BPPM) Approach
### Event Log Generation  
In this stage, it is required to model the data in the form of an event log [28] (i.e., a record of the events that have happened in a process). Formally, an event log is defined as a set of cases (executions of the process), where each case is an ordered sequence of events (the actions occurred in that execution) [28]. Therefore, in order to define an event log, it is necessary to define (1) how to identify a case and (2) how to specify a sequence of events.  
A classic first event log option for curricular data consists of defining each case as a student and each event as a course taken by that student, in the order in which he/she has taken it. For example, <A, Q, C, D, A, Q, A> would define the trajectory of the student with \(s=23\), according to Table 2.  
However, as mentioned above, our BPPM model proposes a different perspective on curricular data, where each event in a student's trajectory is the backpack he or she has at the end of each academic term. Formally, (1) each student identifier in the BPPMt table identifies a different case <b\({}_{1}\), b\({}_{2}\),... b\({}_{n}\)>; and (2) a b\({}_{i}\) event is defined as the record of the group of failed courses that the student must retake at the end of academic period i. For example, for the student identified with \(s=23\) in Table 2, <AQ, Q, -> represents their backpack trajectory and graphically it can be seen in Figure 3. In his/her first academic period (for example, semester), this student had failed algebra (A) and chemistry (Q) and therefore must retake them. In their second period the student must still retake chemistry (either because the student took it and failed it again or because the student decided not to take the course in the second period) and finally, after the third academic period, the student does not have courses that should be retaken.  
For simplicity, the above makes an abuse of notation, where the set {A, Q} is represented by the label AQ and the empty set is presented by the label -. Similarly, an ordering between course identifiers is assumed, such that two equal sets are represented by the same label {A, Q} = {Q, A} = AQ.  
This definition of event log allows us to analyze the trajectories in the backpack. However, a student who stays two academic periods with the same backpack will be represented with two consecutive equal events, where the first event ends in the first period and the second in the second period. To analyze how much time the student maintains the same backpack, it needs to be represented as a single event, which begins at the end of the academic period in which this backpack appears and ends in the period in  
Figure 3: Graphical representation of the sequence of backpacks for the student with \(s=23\), shown as an example in Table 2, according to the BPPM model.  
which the backpack changes. The BPPM model proposes the post-processing of the event log defined above, to merge consecutive events that represent the same backpack. That is, given a case \(<\ldots\) ; b\({}_{\text{i}}\); b\({}_{\text{i+1}}\); \(\ldots\) ; b\({}_{\text{i+n}}\); \(\ldots\) \(>\) where b\({}_{\text{i}}\) = b\({}_{\text{i+1}}\) = \(\ldots\) = b\({}_{\text{i+n}}\), will result in a case \(<\ldots\). b\({}_{\text{i+n}}\). \(>\), where backpack b\({}_{\text{i+n}}\) ranges from period i to period i + n.  
To easily distinguish between cases that ended in dropout or retention, for the backpack trajectories that ended with the empty backpack, in the BPPM model, the \"-\" label was replaced by the label \"RETENTION\" and in the other cases, a \"DROPOUT\" event was added at the end of the case. In the example used in the previous paragraph, \(<\)AQ, A, \(>\), was replaced by \(<\)AQ, A, RETENTION\(>\) in the BPPM event log.  
Finally, to obtain the event log for the BPPM-S model, each b\({}_{\text{i+n}}\) event was labeled with \(BP\)-j, where j represents the size of the backpack. For example, the case represented by \(<\)AQ, Q, RETENTION\(>\), was replaced by \(<\)BP-2, BP-1, RETENTION\(>\) in the BPPM-S event log.