Методы и алгоритмы улучшения представления циклического поведения в моделях процессов, синтезируемых по журналам событий тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Шаимов Никита Денисович

• Шаимов Никита Денисович
• кандидат наук
• 2026

Оглавление диссертации кандидат наук Шаимов Никита Денисович

Contents

Introduction

1 Background

1.1 Process Mining

1.1.1 Process Discovery

1.1.2 Conformance Checking

1.1.3 Performance Analysis

1.2 Basic Notions

1.2.1 Preliminaries

1.2.2 Model Metrics

1.3 Conclusions

2 Discovery of Acyclic DFG Models for Acyclic Processes

2.1 Problem Statement

2.2 Motivating Example

2.3 Related Work

2.4 Proposed Solution

2.4.1 Acyclic Event Log Partitioning

2.4.2 Model Merging Algorithm

2.4.3 Merging Models With Repeated Vertices

2.5 Evaluation

2.5.1 Case Description

2.5.2 Models Assessment

2.6 Conclusions

3 Visualisation of Acyclic Process Models

3.1 Problem Statement

3.2 Motivating Example

3.3 Proposed Solution

3.4 Evaluation

3.5 Conclusions

4 Discovery of Directly-Follows Graph Process Models Without Fake Cycles

4.1 Motivation

4.2 Discovery Algorithm

4.2.1 Step 1: Partitioning an Event Log

4.2.2 Step 2: Merging DFG Models

4.2.3 The First Correctness Theorem

4.2.4 The Second Correctness Theorem

4.3 Experimental Evaluation

4.3.1 Layout of Experiments

4.3.2 Experiment Results and Discussion

4.4 Related Work

4.5 Conclusions

5 Educational Process Mining: Case Study

5.1 Introduction

5.2 Related Work

5.3 Analysis of Exams

5.3.1 Case Description

5.3.2 Trajectory-Based Approach to Educational Process Analysis

5.3.3 Event Log Construction

5.3.4 Methods and Analysis Approach

5.3.5 Evaluation of Metrics

5.3.6 Observations and Findings

5.4 Analysis of Educational Courses

5.4.1 Case Description

5.4.2 Problem Definition

5.4.3 Event Log Construction

5.4.4 Results Evaluation

5.5 Conclusions

Conclusions

Acknowledgements

List of Fugures

List of Tables

References

Appendix A. Russian Translation of the Thesis

Введение диссертации (часть автореферата) на тему «Методы и алгоритмы улучшения представления циклического поведения в моделях процессов, синтезируемых по журналам событий»

Introduction

Information systems are widely used to support processes in various fields, including business, healthcare, and logistics. These systems record data on process execution in the form of event logs. Analysing the data helps organisations understand the observed behaviour of processes and find ways to improve them. A visual process model can reveal patterns, deviations, and inefficiencies, facilitating experts' assessment and optimisation of the process.

Process mining [1,2] methods are designed to extract process-related insights from event logs. One of the central tasks in process mining is process discovery, which involves synthesising a process model that describes the behaviour observed in the data. A wide range of process discovery algorithms have been developed that can synthesise process models in different notations, such as Petri nets, BPMN, UML, and Directly-Follows Graphs (DFGs). The application of these methods has been extensively studied in the literature and covers many domains, including healthcare [3,4], education [5-8], manufacturing [9], and others.

DFG is a simple and widely adopted notation supported by the most popular process mining tools, such as PM4Py [10], Celonis [11], and Disco [12]. It presents the process as a directed graph, where each arc between event vertices shows a directly followed relationship between two event names. This simplicity makes DFG models accessible to users without a technical background.

The DFG notation has several limitations. They cannot represent concurrency, and can lead to misleading structures when applied to certain types of data [13,14]. One of the misleading structures is a cycle that is not present in the event log but can appear in the discovered models. We refer to such cycles as fake. For example, if in an event log an event A directly-follows event B and event B directly-follows event A, this will produce a cycle in the DFG model. There are two cases in which this cycle can be considered fake. In the first case, every sequence of events in a

process does not contain recurring events. In this case, the process is considered acyclic, and the process model must also be acyclic. In the second case, events A or B do not occur more than once in any event sequence of the process. In this case, event A or B is considered non-recurring and must not be part of any cycle in a process model. Fake cycles in a process model allow the reproduction of incorrect behaviour; thus, the model misrepresents the actual process behaviour. To the best of our knowledge, none of the existing process discovery algorithms focus on the correct representation of cyclic behaviours.

The main aim of this thesis is to provide methods and algorithms for enhancing the representation of cyclic behaviour in process models discovered from event logs. The representation can be enhanced both structurally and visually. The correct structural representation can be achieved using the new discovery algorithm. The discovered process models should correctly represent the cyclic behaviour shown in event logs and not contain any fake cycles. The visual representation of cyclic behaviour can be enhanced using visualisation approaches. An acyclic process should be represented using an acyclic model. Acyclic process models offer advantages that can be used for new process model visualisation methods.

Main contributions of the thesis

1. An algorithm for discovering acyclic Directly-Follow Graph (DFG) process models from acyclic event logs. The algorithm discovers DFG process models with perfect fitness.

2. A new visualisation approach for acyclic process models that combines DFG with Sankey diagrams. This approach allows groups of cases to be highlighted in the model.

3. An algorithm for discovering DFG process models without cycles not presented in the event log. The algorithm discovers DFG process models with perfect fitness.

4. Implementation of the discovery algorithms. Experimental evaluation of algorithms on synthetic and real-life data.

Presentation of contributions

The key results of this thesis have been presented and discussed at the following conferences:

1. Spring/Summer Young Researchers' Colloquium on Software Engineering (SYRCoSE-2024, May 2024, Stavropol, Russia).

Talk: Merging Directly-Follows Graphs and Sankey Diagrams for Visualizing Acyclic Processes

2. II Scientific Conference of the Faculty of Computer Science 2024 (October 2024, Moscow, Russia).

Talk: Mining acyclic DFG models for acyclic processes

The results of the thesis were regularly discussed at the scientific seminar hosted by the Laboratory of Process-Aware Information Systems (PAIS Lab) of the Faculty of Computer Science, HSE University.

Publication of contributions

The main results of this thesis are published in the following papers:

1. Shaimov N.D., Lomazova I.A., Mitsyuk A.A., Samonenko I.Yu. Analysis of Students' Academic Performance using LMS Event Logs // Modeling and Analysis of Information Systems. 2022. Vol. 29. No. 4. P.286-314.

2. Derezovskiy I.D., Shaimov N.D., Lomazova I.A., Mitsyuk A.A. Merging Directly-Follows Graphs and Sankey Diagrams for Visualizing Acyclic Processes // Proceedings of the Institute for System Programming of the RAS (Proceedings of ISP RAS). 2024. Vol. 36. No. 4. P.155-168.

3. Shaimov N.D., Lomazova I.A., Nesterov. R.A. How to Prevent Fake Cycles in DFG Models Discovered from Event Logs? // Programming and Computer Software. 2025. Vol. 51. No. 6.

Thesis Outline

The main part of the thesis consists of five chapters. Chapter 1 introduces the research area and contains definitions of the basic concepts used in this thesis. Chapter 2 describes an acyclic DFG discovery algorithm for acyclic processes. Chapter 3 contains a visualisation approach for acyclic process models based on DFG and Sankey diagrams. Chapter 4 presents a DFG discovery algorithm without fake cycles. Chapter 5 provides a case study of an educational process that consists of two parts. The first part presents an analysis approach using existing process mining methods. The second part shows where the existing methods are lacking and how the methods and algorithms provided in this thesis can be used. Related research is discussed separately in the corresponding sections of Chapters 2, 4, and 5.

Заключение диссертации по теме «Другие cпециальности», Шаимов Никита Денисович

Основные результаты диссертации

В данной диссертации предложены методы и алгоритмы для улучшения представления циклического поведения в моделях процессов, обнаруженных на основе журналов событий.

Предложенные в диссертации алгоритмы обнаружения процессов позволяют синтезировать модели с более точным представлением циклического поведения за счет предотвращения появления фальшивых циклов в моделях. Фальшивые циклы предотвращаются за счет допускания нескольких вершин для одного и того же события. Синтез модели включает в себя разбиение журнала событий на части, а затем объединение моделей полученных поджурналов. Во время слияния предотвращение фальшивых циклов достигается путем введения нескольких вершин для одного и того же события, где это необходимо. Алгоритмы были протестированы как на реальных, так и на синтетических данных. Модели, синтезированные с помощью алгоритмов, идеально соответствуют журналу событий и в целом демонстрируют более высокий уровень точности по сравнению с моделями, синтезированными с помощью существующего алгоритма обнаружения DFG. Первый алгоритм ограничен ациклическими процессами и быстро создает модели с максимальной точностью. Второй алгоритм может быть применен к любому процессу для создания более компактных моделей за счет времени и точности.

Модели ациклических процессов могут быть усовершенствованы с помощью подхода визуализации, который сочетает структуру DFG со стилем потока диаграмм Санки. Существующие визуализации требуют параллельного сравнения двух моделей для сопоставления группы кейсов с остальными. Подход визуализации на основе потока позволяет выделять определенные группы непосредственно на модели. Группы определяются набором критериев, который позволяет отображать несколько групп кейсов и их пересечения. Модели, созданные алгоритмами для ациклических процессов, также являются ациклическими. В сочетании с визуализацией ациклический процесс может быть представлен в виде ациклической модели потока кейсов.

Направления дальнейших исследований

В рамках дальнейших исследований возможно улучшение сложности алгоритмов с точки зрения времени и памяти за счет различных оптимизаций. Постоянство результатов можно улучшить за счет уточнения эвристических частей алгоритмов. Подход к визуализации можно дополнительно улучшить, чтобы отображать циклическое поведение. С помощью предложенного подхода можно отображать циклы, однако это может затруднить восприятие модели. Подход может быть дополнительно адаптирован к другим типам моделей процессов. Например, модели, основанные на объектно-ориентированных журналах событий (OCEL), могут извлечь выгоду из представления моделей в виде потока. Наконец, алгоритмы и подход к визуализации могут быть включены в инструмент для анализа процессов, который может служить практическим инструментом для аналитиков процессов.

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