Step 1: Business Process Discovery

Process mining has multiple perspective to analyse the behaviour of processes in systems. One of the perspective is control-flow perspective, with goals to find a good characterisation of all possible paths of processes. Usually this perspective expressed in terms of a Petri net or other notation (i.e, BPMN, UML activity diagram) [36]. In this research, we want to incorpo- rate one of the control-flow perspective algorithm to discover business processes that resides

in logs of systems of an enterprise. We called this mechanism asbusiness process discovery

algorithm, to discover business process that resides in logs, that enable us to observe busi- ness process behaviour of systems. This algorithm will be the backbone of our EA mining and as a foundation for extending other EA mining algorithms. We used heuristic miner (Def- inition.10) as a baseline for the algorithm, and the algorithm result limited to Archimate. We chose Heuristic miner since it is enable us to discover processes and its concurrences and also its capabilities to deal with noise (low frequency activities) and infrequent/incomplete activities.

Heuristic miner produces dependency graph (Definition.15) as its process model [44], the dependency graph represents all the dependencies found in the log. Fig.4.6 is an example of dependency graph that resulted from a heuristic miner processing. As can be seen at the figure, it has rectangle to represent an activity with its frequency occurrences, the arc rep- resent dependency path between activities, the arc also has label that represent dependency factor and its frequency. We proposed the conversion pattern in the literature study chapter

(Section.2.2.4) and the result ofbusiness process discoveryalgorithm is similar to the depen-

dency graph, and instead of rectangle as an activity, we substitute it withbusiness process

element, and we convert arcs toservingrelationship. Example of the converted graph can be

Figure 4.6: Example dependency graph [44]

Figure 4.7: Example of converted dependency graph to Archimate

Definition 15(Dependency Graph [4]). Given a set of activities V and a log of executions L of the same process, a directed graph𝐺 is a dependency graph if there exists a path from activity u to activity v in𝐺 if and only if v depends on u.

The input for this algorithm is the log structure (Section.4.1.1), which complies to the definition of simple event log (Definition.4). The simple event log is subset of the log structure, since the input for this algorithm focuses only on activity name of events. Thus we defined

business process discovery as follows:

Definition 16(Business Process Discovery). Let L be an event log over activities of T, with trace of𝜎.

Step 1. Identify activities in the log

𝑇 = {𝑡 ∈ 𝑇 ∣ ∃ ∈ 𝑡 ∈ 𝜎}.

The first step of the algorithm is to identify activities in the event log. Assuming that we have an event log of𝐿 = [(𝑎, 𝑐, 𝑑) , (𝑏, 𝑐, 𝑑) , (𝑎, 𝑐, 𝑒) , (𝑏, 𝑐, 𝑒) ],(𝑎, 𝑐, 𝑑)is a trace, while ”a” in(𝑎, 𝑐, 𝑑)

denotes an activity (attribute) of an event. By applying the step 1, activities will be𝑇 = (𝑎, 𝑏, 𝑐, 𝑑, 𝑒).

Step 2. Constructing activities sequences

In step 2, the algorithm will produce activities sequences of a trace in the event log, using the following sub-step:

a. 𝑎 > 𝑏iff there is a trace𝜎 = 𝑡 𝑡 𝑡 ...𝑡 and𝑖 ∈ {1, ..., 𝑛 − 1}such that𝜎 ∈ 𝐿and𝑡 = 𝑎 and

𝑡 = 𝑏,

b. 𝑎 → 𝑏iff𝑎 > 𝑏and𝑏 ≯ 𝑎, c. 𝑎# 𝑏iff𝑎 ≯ 𝑏and𝑏 ≯ 𝑎, d. 𝑎|| 𝑏iff𝑎 > 𝑏and𝑏 > 𝑎,

By applying Step 2a, the algorithm will determine which activities appeared in sequence, for ex- ample of𝐿 , it will produce(𝑎 > 𝑐, 𝑐 > 𝑑, 𝑏 > 𝑐, 𝑐 > 𝑑, 𝑎 > 𝑐, 𝑐 > 𝑒, 𝑏 > 𝑐, 𝑐 > 𝑒). 𝑎 > 𝑐

denotes that activity c will follow activity a. Relation→ denotes a direct dependency relation, using the definition of Step 2b, we identified direct dependency relationship between activities. Relation|| denotes concurrent behaviour, or potential parallelism between activities. We used Step 2d, to identify this behaviour. While# denotes two activities never follow each other directly. The summarization of all behaviour activities of𝐿 can be seen at Table.4.2.

Step 3: Create a frequency matrix

We count occurrences for each sequence of activities𝑎 → 𝑏and produce a frequency matrix. An example of the matrix of𝐿 can be seen at Table.4.3.

Step 4: Create a dependency matrix

Using formulation of 𝑎 ⇒ 𝑏 = ( | | | |

| | | | ) (Definition.11), we can generate dependency matrix of each activities, the dependency matrix for𝐿 can be seen at Table.4.4.

Step 5: Create a result matrix

To simplify the result of the algorithm, we combine all the information from step 2-4 and produce a matrix that consists of sequence of activities with columns source and target, with its frequency and dependency factor. Table.4.5 is an example of result table using the log of𝐿 and if the result converted into a converted dependency graph it becomes Fig.4.8.

Table 4.2: Footprint of a b c d e a # # → # # b # # → # # c ← ← # → → d # # ← # # e # # ← # #

Table 4.3: Frequency matrix of

a b c d e a - - 83 - - b - - 64 - - c - - - 87 60 d - - - - - e - - - - -

Table 4.4: Dependency matrix of

a b c d e a - - 0.99 - - b - - 0.98 - - c - - - 0.99 0.98 d - - - - - e - - - - -

Table 4.5: Finalise table

source target frequency dependency

a c 83 0.99

b c 64 0.98

c d 87 0.99

c e 60 0.98

Figure 4.8: EA model conversion of