# Experimental Analyses of Temporal Activity-Sequencing Anomalies in Process Mining
## 3 Temporal Activity-Sequencing Anomaly Detection Approach
### The Origin of Temporal Activity-Sequencing Anomalies  
This paper uses this ICN-based modeling approach to formalize and deploy the theoretical concept of the temporal activity-sequencing anomalies and their noises. In the ICN-based process modeling approach, there are four types of primitive routing (control flow) patterns, as follows:  
* Sequential control-flow: Activity follows activity by a sequential order.
* OR control-flow: In the Or control-flow, an activity (or decision) has a disjunctive transition followed by two or more activities. Only one of the followed activities will be executed next.
* AND control-flow: In the And control-flow, an activity has a conjunctive (or parallel) transition followed by two or more activities. All of the followed activities will be executed next.
* LOOP control-flow: In the Loop control-flow, an activity has a loop transition. The activities inside the loop area will be executed repeatedly.  
Let us assume that the process-aware information system correctly records all the business process instances and their workitem enactment event logs. Then, each of the business process instances produce an event trace representing the temporal ordering of the activities' event logs. The four primitive process routing patterns are used in the ICN-based business process modeling methodology and the possible workcases instantiated from each of the process routing patterns will look like the following:  
* Sequential workcases: ABCD, ABCD,...
* OR workcases: ABD, ACD, ACD, ABD,...
* AND workcases: ABCD, ACBD, ABCD,...
* LOOP workcases: ABCD, ABCBCD,..., A(BC)'D  
In particular, the workcases of the AND and LOOP process-routing patterns are involved in the temporal activity-sequencing anomalies when each workcase forms a temporal activity-sequencing workcase model to be applied into \(\rho\)-Algorithm [11]. In the AND workcases, every workcase has a pair of mutual orderings between activity B's event logs and activity C's event logs such as BC and CB in ABCD and ACBD, respectively. However, these temporal orderings of BC and CB are nonexistent edges in the original AND process-routing pattern. The author names these nonexistent edges as AND-Anomalies. In principle, activity B and activity C are simultaneously followed by AND control-flow split-gateway, which implies that both activity B and activity C must be performed in parallel right after performing activity A. In the LOOP workcases, every workcase has a pair of iterative orderings with activity B's event logs and activity C's event logs such as BCBC and BCBCBC. As we know, however, the temporal orderings of CBs in LOOP workcases are nonexistent edges, too, in the original LOOP process-routing pattern. These situations result in the innate anomalies with the temporal orderings of activity B and activity C in the AND process-routing pattern as well as the temporal orderings of activity C and activity B in the LOOP process-routing pattern.  
Consequently, these nonexistent orderings associated with AND and LOOP workcases become the origin of the temporal activity-sequencing anomalies and noises, and ultimately bring about debasing the level of correctness and quality of the process-mining algorithm and system. Therefore, this paper aims at the cause-and-effect analysis of the temporal activity-sequencing anomalies by performing a series of experimental analyses on a group of process-enactment event log datasets provided by the 4 TU.ResearchData, which is an international data repository for science, engineering, and design [5]. It is worth noting that the authors' research group has successfully devised a temporal activity-sequencing anomaly detection and removal algorithm and applied said algorithm to a process-mining algorithm (\(\rho\)-Algorithm) [11]) and its implemented system.