# CONDA-PM--A Systematic Review and Framework for Concept Drift Analysis in Process Mining
## 2 Fundamentals
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case ID**} & \multirow{2}{*}{**Event ID**} & \multicolumn{4}{c}{**Properties**} \\ \cline{3-6}  & & **Timestamp** & **Activity** & **Resource** & **Cost** \\ \hline \multirow{4}{*}{\(1\)} & 3561 & 30 December 2018 10:02:15 & Enter Loan Application & [PERSON] & 120 \\ \cline{2-6}  & 3562 & 31 December 2018 09:08:22 & Retrieve Applicant Data & [PERSON] & 100 \\ \cline{2-6}  & 3563 & 1 January 2019 12:20:00 & Compute Installments & [PERSON] & 80 \\ \cline{2-6}  & 3564 & 5 January 2019 10:10:28 & Notify Eligibility & [PERSON] & 150 \\ \cline{2-6}  & 3565 & 10 January 2019 08:30:10 & Approve Simple Application & [PERSON] & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A fragment of some event log. _An event stream in turn, corresponds to a collection of events that were created in the context of running process instances._ Each event has an embedded identifier to enable matching it with the corresponding activity this event belongs to. In this sense, a log file is a complete record of an event stream. An entry of the log file has a start and an end event, whereas an event stream represents an incomplete running process instance [3]. **Definition 3** (Process perspectives). : _The data captured in an event log describe a business process from different perspectives [2]:_  
* _Control-flow perspective,_ that is, order of activities. Mining this perspective allows characterising and exploring possible execution paths of a process. * _Organisational perspective,_ that is, organisational resources and roles involved in the occurrence of events. Mining this perspective enables the discovery of the social network and the roles participating in a business process. * _Time perspective,_ that is, the point in time events occur. Mining this perspective enables finding bottlenecks and monitoring key performance indicators (KPI) of a business process. * _Case perspective,_ that is, properties of process instances (e.g., values of data elements characterising a process instance). Mining this perspective enables understanding contextual information specific to the current process instance. **Definition 4** (Process history and process variants). : _A process history represents a list of viable process models discovered for one business process [3]._  
The process models are discovered at different points in time whenever a violation from the normative process model is detected. The latter is accomplished through checking the conformance of events against the most recent process model from the process history. _A process variant,_ in turn, corresponds to _a subset of process instances recorded in an event log._ These process instances have some commonalities (e.g., sharing certain activities with each other), but also show differences to process instances corresponding to other process variants [4]. Process histories are more concerned with the flexibility of a process at the instance level, whereas process variants are studied in the context of business process variability. **Definition 5** (Execution graph, REGs). : _An execution graph is a directed acyclic graph used to represent the execution of a process instance in terms of nodes (i.e., events), edges (i.e., relations between the nodes),