# Understanding Contrail Business Processes through Hierarchical Clustering: A Multi-Stage Framework
## 1 Introduction  
Business processes in the real-world context typically consist of several information sources and various process flows. To execute these business processes, Process-Aware Information Systems (PAIS) [1], such as customer services, healthcare, education, and banking systems, operate in a constantly evolving business environment. Process mining techniques have been developed to analyse these logs and understand the behaviour of varied process flows. Analysis of complex business processes reveals that many business subcategories are integrated into the event log [1]. Real-world business processes also go through recursive improvement measures which bring change in the way a process executes, adding more uncertainty in the flow. Many techniques have been introducedby researchers that allow the exploration of process data to discover the underlying process model. Furthermore, conformance checking techniques, such as token replay and process alignments, are used to compare the discovered model with actual events. These techniques allow enhancement of the process by recommending the necessary changes [2]. Process discovery is the first step towards mining and improvement of a business process. For more than a decade, researchers have introduced several techniques for discovering underlying process models using an extracted log, termed as replay [3]. For so-called lasagna processes, where the number of events and tasks are not large and where the process is structured, process modelling is a reliable technique for process discovery [4]. However, for more complex processes, such as spaghetti processes, it is vital to first decompose the large heterogeneous process log into small, manageable, and meaningful classes. Once done, further exploration of the log is more straightforward and can follow traditional process mining steps [5]. Things become more complicated when the process operates in an established real-world business environment and adjustments towards achieving business goals tend to change the process regularly [6]. This change is normally brought about by human intervention and is mostly for specific cases, for example, changing the pre-requisites of a course for specific students in an academic environment, or allow students to apply for medical leave through an online portal where the process normally expects a hard copy of the doctor's prescription. Trace clustering [3] techniques discover similarities in the process flow by exploring the events data. Trace clustering helps to group similar cases within the given process and thus obtaining a deeper insight into each cluster of event data. Another approach used by researchers to explore event data is rule-based mining which discovers the sequential patterns between the events of the process. It helps to gain knowledge about the nature of the process and exploring possible similarities between the instances. The literature suggests that, so far, trace clustering and rule-based mining are not widely used in scenarios such as, (i) unlabelled process data, (ii) processes with highly integrated business classes, such as customer services in the telecoms sector,(iii) hybrid processes which present the characteristics of both lasagna and spaghetti processes at the same time, and (iv) processes with very large numbers of events in each process instance. For instance, studies such as [3; 4; 5] used process log with average event size of less than 10. In this paper, process discovery is performed by using a multi-stage framework through a proposed algorithm Novel Hierarchical Clustering (NoHiC) (Algorithm 1) that combines the methodologies of both, process modelling and unsupervised machine learning. Techniques such as Rules-based mining [6] and hierarchical clustering of the process instances [6] are proposed for simplification of large and complex real-world business processes, which are described in this paper as contrail processes (Section 3.1).