## 1 Introduction  
In recent years, both researchers and practitioners have been applying learning analytics to support curriculum understanding and improvement [1, 2]. Worldwide participation in higher education has grown around the world [3]. However, the number of graduates in undergraduate programs remains low, and pressure is being placed on universities in many countries to increase the number of graduates in order to meet the needs of society [4]. The main focus on dropout research has been on early dropout [5]. However, the problem of late dropout has been gaining importance in higher education [6]. Different methods have been used to understand and predict the dropout phenomenon. Qualitative techniques include surveys and in-depth interviews [7, 8], whereas quantitative techniques include a broad range of statistical and data mining methods, such as neural networks [9], multinomial logistic regression [10, 11], genetic algorithms [2], and event history analysis [6, 12]. The application of longitudinal analysis techniques [12] has also shown that the risk of dropout changes over time and that dropout does not generally occur as a spontaneous event, but rather as a consequence of a particular process [13]. Although event history analysis can help to understand the relationship between each variable and an outcome across time, sequences of events that include cycles, called swirling patterns [11], are not sufficiently well described by this kind of models. Learning analytics (LA) is a growing research area, whose purpose is the measurement, collection, analysis, and reporting of data about students and their learning processes [14]. Recent research shows the importance of a more holistic approach to improve the efficiency and effectiveness of learning programs, focusing the analysis to the program level [15]. Curricular analytics (CA) has emerged as a sub-field of LA, aiming to use evidence to drive curriculum decision-making and program improvement [1, 16]. CA uses data both at course-level and program-level, to analyze the interactions between students and the curriculum along time [1]. This understanding can help to identify points in the program structure where interventions are more relevant to improve student progression [15]. In this work, we are interested in understanding the educational trajectories of students, using CA techniques. In particular, this study defines an educational trajectory as a _process_, i.e., a set of events that occur in a certain order during the permanence of the students in a given program. In this study, we focus on analyzing late dropout using Process Mining [17], which aims to extract knowledge from event logs obtained from information systems, in order to discover process models, verify conformance, and suggest improvements [17]. The main difference between Process Mining and other data-centric techniques is the starting point of the analysis. Process Mining is process-centric, whereas statistical and data mining methods are data-centric [18]. The advantage of the process-centric approach lies in that it supports a more holistic comprehension about the process (in this case, the educational trajectory), using graphical and analytical tools [17]. These kinds of models facilitate visual cognition and make understanding of sequences of events more efficient [19]. In this work, Process Mining allows us to study the dynamic behavior of educational trajectories so as to understand which educational trajectory patterns lead to late dropout and which ones do not. Process Mining has been applied in multiple domains, with particular success achieved in fields in which processes are insufficiently structured, as is the case in education [20], although applications of Process Mining at the curricular level have been less frequent [21]. This paper is structured as follows. Section 2 introduces the literature on dropout and two related theoretical frameworks. Section 3 presents the research question. Section 4 presents the materials and methods. Section 5 summarizes the main results.