# Process Discovery for Event Logs with Multi-Occurrence Event Types
## 2 Related Works  
### Process Discovery  
The automatic workflow schema induction is a complex process; it requires the integration of more processing modules. One of the key components is the mining of frequent subsequences in the event log. The field of frequent path mining is also of interest in many domains. For example, [PERSON] et al. developed an algorithm for sequence prediction over long categorical event streams [16]. [PERSON] [17] and [PERSON] [18] propose methods to extract temporal patterns in industrial alarm management systems. Analyzing study paths for the prediction of student dropout [19] and identifying efficient learning patterns in e-learning environments [20,21] are key concepts in educational data mining. In these examples, frequent patterns are selected based on their utility. In [22], the authors argue that the cost perspective should also be considered when mining event sequences. The drawbacks of the traditional frequent pattern mining solutions come to the surface when dealing with massive datasets [23]. The algorithms have problems with runtime and accuracy [24], and their output data are difficult to interpret and handle [25]. In order to efficiently mine frequent patterns, a tree-based representation has proved to be more compact and, practically, more usable [26]. For this purpose, [PERSON] et al. proposed the FUSP-tree structure [27], which gave rise to numerous variations of incremental tree-based pattern mining algorithms [28, 29, 30, 31]. A more efficient approach is to apply incremental discovery, which derives event patterns recursively. Another representation model was proposed by [PERSON] [32], who introduced a directed acyclic graph representation, which allows for pattern growth along both ends of the detected patterns. This algorithm ensures a faster pattern discovery, too. The work of [PERSON] and [PERSON] [33] combines the graph-based approach with the clustering of patterns to avoid the recursive reconstruction of intermediate trees. [PERSON] et al. [34] use a graph-based approach to extract frequent sequential web access patterns, while [PERSON] et al. [35] present a new weighted graph structure and a method to find variable-length sequential patterns. The first proposals on process discovery were published in the late 1990s [36]. The first widely used method is the alpha miner [37]. The alpha-miner algorithm generates a Petri net schema result in the following steps:  
* Discovering distinct events;
* Discovering starting and final events;
* Grouping the events and constructing a footstep matrix to show direct succession, parallel, and choice control structures;
* Determining the schema nodes and connecting them. In the literature, we can find many application use cases of the alpha miner, including modeling educational processes [38], clinical workflow analysis [39], and software engineering [40]. The inductive miner [41] is an improved powerful process discovery algorithm. It applies a structured, divide-and-conquer approach. The method produces correct valid process models in the form of block-structured models (process trees and Petri nets). The approach processes the trace sequence recursively; the method splits the large input log into smaller segments, generates models for the segments, and finally, merges the local models into a global final model. Regarding the recent research directions, the main focus areas relate to adaptation of the method to large-scale problems using a simplified, approximated model [42]. The heuristic miner generates the workflow schema based on probabilistic models using dependency frequency measures [43]. The main steps of the workflow model construction are the following:* Building the dependency graph;
* Constructing the causal matrix to represent the correct process model. One key benefit of this approach is that this model can handle small noises in the event logs. A recent comparative analysis of the different process discovery algorithms was presented in [44].