# Process Discovery for Event Logs with Multi-Occurrence Event Types
## 2 Related Works
### Limitations of Current Process Discovery Methods  
Considering the traditional, automaton-based process discovery methods, all the leading methods are based on some form of the Directly-Follows Graph (DGF), which is a directed graph that represents the sequence of activities. Process mining practitioners tend to use such simplified DFGs actively. In order to scope with complexity, DFGs are usually simplified by many ways [58]. One standard method is the removal of infrequent nodes and edges. Another approach is to assume that the type of event node is identified uniquely and, thus, every node type has a unique node in the DFG and in the generated schema graph. In some real application fields, especially with an imperfect information background [59], this uniqueness assumption cannot be guaranteed. In these cases, the resulted schemas are incorrect and misleading. Another source of confusion is the multi-occurrence of a given event type inside the traces. The same event type may have different prefix and postfix sequences at the different positions. The mapping the different subtypes to the same event type causes over-generalization. In this case, the schema generates hallucinations and invalid traces. Beside theses simplification assumption, another key issue is the complexity limitations of the standard methods. Due to the inherent algorithmic nature of the automaton approaches, the detection of complex, deeper nested structures is a great challenge, and the current methods are not able to manage these complex structures within an acceptable time.  
Based on these shortcomings, there is intensive research on the efficiency improvement of the process discovery methods, focusing mainly on the application of machine learning methods, in the recent years. Although there are many promising results, the current technology is far from perfect. Summarizing the current achievements, we can highlight the following approaches:  
* Current industry level solutions (like alpha miner, inductive miner, or heuristic miner) are universal tools, but they cannot scope with event type multi-occurrences and deeper nesting.
* Application of recurrent neural networks (LSTM) for process discovery [60]. The model is strong at finding XOR patterns, but weaker at discovering loops or event type multi-occurrences.
* There are only a few methods for process mining using graph neural networks technology. The most recent approach [61] applies the GNN for extension of the DFG approach; the proposed method is not suitable to manage the problem of event type multi-occurrences. The main reason for the lack of more GNN -based solutions is that the GNN architecture is mainly focusing on the manipulation of edges and nodes inside a fixed input graph. The generation of a new graph from very different graph pieces requires a novel GNN architecture.  
The main goal of our investigation is to address these shortcomings and to provide a new proposal for a process discovery approach which integrates both machine learning components and traditional graph methods. The proposed method applies convolutional neural networks (CNN) for fuzzy loop detection and similarity calculation. As the GNN is the standard tool for link prediction in the graph, we apply the GNN approach for finding the equivalent event instances of a given event type and, then, we employ standard quasi-clique graph detection methods to determine the event nodes of the resulting schema graph.