# CONDA-PM--A Systematic Review and Framework for Concept Drift Analysis in Process Mining
## 5 Concept Drift Analysis Approaches in Process Mining
### Approaches Based on Windowing and Statistical Analysis  
A common theme which distinguishes this category of approaches in their reliance on statistical approaches to detect changes in event logs divided into windows of either fixed or changeable sizes. The authors of [35] present an approach based on abstract interpretation. It adapts an abstract domain of _convex polyhedra_. A _Parikh vector_ is formed representing the number of occurrences of activities in a certain trace. Note that parikh vectors are used for representing features upon which the traces will be classified as belonging to certain polyhedron. Note that this approach is only able to detect the occurrence of a change, but cannot localise it. Furthermore, it depends on the number of occurrences of activities to characterise a trace without regarding other behavioural aspects manifested through the trace (e.g., the relations between its activities). Corresponding experiments were conducted in a fully artificial situation, neither with considering multiple overlapping drifts nor drifts that may not affect the resulting Parikh vectors in an observeable manner (e.g., parallelism of activities or changing ordering relations between activities). This method was criticised by the authors of [21; 31] for its inability to detect multiple drifts at the same time, its poor performance [31], and its inability to pinpoint the exact moment of the drift. In [13], an event log is divided into _time-based windows_. Based on this division, feature vectors are defined either locally for each trace or globally for a subset of the log. The features are used to characterise the current situation of relations between pairs of activities. Furthermore, these features can be also used to detect a change whenever a difference in these relations occur. The authors consider a series of successive populations, whose size is predefined as windows. Then, the differences between two populations are manually investigated. The authors of [31] criticize the need for user interventions by specifying the features used for drift detection as well as the unsuitability of the approach for identifying certain types of drifts, for example, the insertion of conditional branching in a process model. The authors of [21] modify the approach presented in [13] by using adaptive analysis window size, that is, the number of traces to be compared may be adapted. Furthermore, the authors of [21] propose an approach for _automatic change point detection_ through comparing significance values of two populations against a pre-specified threshold. Hypotheses analysis is used to produce these significance values. The basic contribution includes the analysis of gradual drifts as well as the detection and localisation of multi-order dynamics. Experiments prove that runtime and size of steps between windows are inversely proportional [21]. However, increasing step size has a negative effect on the amount of gained information. Although the authors of [21] claim addressing the multi-order dynamics perspective of concept drift, The authors of [21] consider it from both time and granularity sides. Note that the situation would be different if there is an overlap between different types and forms of drifts. The question is whether or not the proposed approach is able to distinguish different drift patterns. In the experiments, the approach in [21] does not include an examination of whether the approach is able to detect and localise multi-order drifts when the length of time intervals between traces arrival is not fixed. Finally, the approach in [21] requires intervention of users with prior knowledge of the type of the drift to be detected; if a gradual drift shall be detected, then the user needs to set a minimum and a maximum gap [9]. An approach that overcomes the limitations observed in [13] and [21] is proposed in [9]. This approach can detect both sudden and gradual drifts from the same event log.