## 1 Introduction  
Process mining [1] integrates various business processes by modeling, managing, controlling, and optimizing the entire lifecycle of the business process. Research on process mining focuses on analyzing event data recorded during the execution of business processes. Process discovery is the basic research direction in process mining. Process discovery technology aims to generate a business process model through the information contained in event logs. However, in the actual process of process execution, there are some random positioning activities that do not belong to the process itself, which are called chaotic activities. The process model is obtained by process discovery technology. The existence of chaotic activities greatly affects the quality of the process model. The occurrence probability of chaotic activities is not affected by other activities, and the occurrence of chaotic activities does not change the occurrence probability of other activities. Therefore, when there is chaotic activity in the event log, the process of the process model found from the event log is very complex, and the existence of chaotic activity will lead to an excessive generalization of the resulting model.  
In practical scenarios, to obtain good quality process models, it is important to pre-process the event log, that is, to improve the quality of the model by identifying activities, events, or traces that affect the quality of the process model and deleting them. Similar event log preprocessing methods also include filtering noise and low-frequency activities. The traditional filtering method filters the chaotic activity in the event log by filtering the noise or infrequent activity, but these methods have some shortcomings. It has been proposed in the literature [2] that chaotic activities can be identified and filtered by calculating activity entropy. However, this method calculates the entropy of each activity by traversing each activity in the log, and then identifies and removes one chaotic activity in each filtering step through the entropy of each activity until there are two activities left in the log. Because this method uses an iterative method to delete the most chaotic activities from the log in each round of the filtering algorithm, and the calculation of entropy is complex, the process of chaotic activity filtering for event logs containing many trajectories and activities takes a lot of time, and the efficiency of this method is low in chaotic activity filtering.  
In this paper, new chaotic activity filtering approaches based on the direct following relationship between activities are proposed, and chaotic activities are identified by using the algorithm to count the direct following relationship between each activity and other activities. Firstly, the direct following relationship between activities in the log is calculated, and then the chaos degree of each activity in the log and the influence of the existence of activities in the log on the total chaos degree of the log are obtained. Finally, the obtained results are used to set conditions to judge whether the activity is chaotic. Experiments show that the approaches can give consideration to both accuracy and running time.  
The first section of this paper introduces related work, the second section introduces two filtering approaches based on a direct following relationship, the third section introduces the comparative experiment between the proposed method and the traditional method, and the fourth section summarizes the article.