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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Analysis in Process Mining</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Yang Lu</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="editor">
          <string-name>Process Mining, Process Discovery, Complex Behaviours Detection</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>School of Computer Science, The University of Sydney</institution>
          ,
          <addr-line>Sydney, NSW 2006</addr-line>
          ,
          <country country="AU">Australia</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Process mining builds a bridge between traditional process modelling and data mining. Process discovery algorithms aim at constructing process models automatically from event logs. Existing process discovery algorithms perform well with simple event logs, but their performance can be afected when the input event logs contain complex behaviours, and the discovered process models may not represent the real behaviours of the business processes. In this research, we plan to develop methods to automatically detect diferent complex behaviours in event logs. The detection of complex behaviours can be based on the extensions of existing process discovery algorithms or stand-alone complex behaviours detection tools. The paper presents our research questions, methodologies, current research progress and potential challenges.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Process mining is a relatively new subject which builds a bridge between traditional process
modeling and data mining [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Process discovery is the most critical part of process mining
which aims at extracting process insights of a system. The discovered process models should
not only have high quality measures (i.e., fitness, precision and generalization), but also be an
accurate representation of the real process behaviours.
      </p>
      <p>
        Many process discovery algorithms have been proposed, and some can return process
models with high fitness and precision values [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. However, when input logs contain complex
behaviours, the discovered models may not describe the process behaviours accurately. Firstly,
some process discovery algorithms cannot guarantee the soundness of discovered models. When
complex behaviours are included in event logs, they may return process models which are
not sound [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. Secondly, in order to accommodate complex process behaviours in a single
process model, process discovery algorithms may return a complex and incomprehensible
process models [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. For example, when the event log contains information of several
microprocesses, it is hard to use a single process model to describe the processes [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. Thirdly, due
to the representation bias [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] of process modeling languages (eg., Petri nets, BPMNs, Process
trees), some process behaviours may not be able to be accurately presented. For example, if an
activity happens in the context rather than in the control flow of the process (i.e., the activity
can happen at anytime during the process), it cannot be accurately described by traditional
process modeling languages [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Lastly, even though a comprehensive and structured process
model is discovered, it assumes the process to be static and may ignore the changes of the
process during the execution time [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ].
      </p>
      <p>
        To discover comprehensive process models, many event log filtering tools have been proposed
[
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] to simplify the event logs. Although event logs can be simplified by using log filtering tools,
important knowledge about the processes can be ignored.
      </p>
      <p>As a goal of process mining is to facilitate business process improvement taking the advantage
of event logs, it is important for us to get deep understanding about business processes. Filtering
out and ignoring complex behaviours in event logs is inappropriate.</p>
      <p>To this end, the proposed PhD project focuses on the detection and analysis of diferent
complex behaviours in event logs. The research questions are presented below:
• Can we extend existing process modeling languages to present diferent complex
behaviours?
• Can we extend existing process discovery algorithms to discover diferent complex
behaviours?
• Can we develop stand-alone tools to discover diferent complex behaviours directly from
event logs?</p>
      <p>On the one hand, existing process discovery algorithms can be extended to handle complex
behaviours. By extending existing process discovery algorithms, their advantages can be
inherited. On the other hand, stand-alone tools to discover diferent complex process behaviours
can be developed. These tools can be applied before performing data pre-processing and process
discovery algorithms to help us understand the complex behaviours ignored by the discovered
model.</p>
      <p>The rest of this paper is structured as follows: Section 2 is a literature review of related work.
Section 3 presents our research approach. Section 4 presents our current research progress.
Section 5 presents potential challenges of our research project and concludes the paper.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <sec id="sec-2-1">
        <title>2.1. Extending Existing Process Modeling Languages and Discovery</title>
      </sec>
      <sec id="sec-2-2">
        <title>Algorithms to Handle Complex Behaviours</title>
        <p>
          The original alpha algorithm [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ] is one of the earliest process discovery algorithms. It guarantees
to rediscover the process model when the event log satisfies certain conditions. However, the
process behaviours which can be discovered by the original alpha algorithm are limited. The
original alpha algorithm has been extended to handle complex behaviours such as the short
loops [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ], invisible tasks [
          <xref ref-type="bibr" rid="ref11 ref12">11, 12</xref>
          ] and non-free-choice behaviours [
          <xref ref-type="bibr" rid="ref11 ref13">11, 13</xref>
          ]. These algorithms
allow complex behaviours to be discovered while maintaining the guarantees of the original
alpha algorithm.
        </p>
        <p>
          The inductive miner [
          <xref ref-type="bibr" rid="ref14 ref15">14, 15</xref>
          ] is one of the most popular process discovery algorithms which
guarantees to return sound process models. Given the direct outcome of the inductive miner is a
process tree, the behaviours being represented are limited. A so-called ”flow model” (i.e., process
model with high fitness but very low precision) can be returned when the process behaviours
are unable to be represented by process trees. To allow more behaviours to be represented and
discovered, both the inductive miner and process tree are extended. For example, Leemans et
al. [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ] extend the inductive miner to discover cancellation behaviours, Lu et al. [17] extend
the inductive miner to discover switch behaviours (i.e., change of paths on exclusive choice
branches). Leemans et al. [18] also extend the inductive miner to discover recursive behaviours
in the execution of software source code. In all these extensions, the discovered models are
always sound.
        </p>
      </sec>
      <sec id="sec-2-3">
        <title>2.2. Stand-alone Tools to Discover Complex Behaviours</title>
        <p>
          Many methods have been developed in order to cluster traces in event logs [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ]. Traces with
similar behaviours are put into the same cluster. Instead of using one process model to represent
the process in the event log, a separate process model is discovered for each cluster.
        </p>
        <p>Besides trace clustering algorithms, some methods also focus on the discovery of hierarchical
process models to handle complex event logs with many activities and sub-processes (eg.,
[19, 20]). A high-level process model can be used to represent the relationship between diferent
sub-processes while a low-level model can be used to represent the process model of each single
sub-process.</p>
        <p>
          To deal with changes within business processes, various methods have been proposed to
deal with concept drifts in event logs [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ]. Some algorithms focus on detecting the time points
of concept drifts (eg., [ 21, 22]). Others focus on providing comprehensive results to users (eg.,
visualise process changes [23]). When time points of concept drifts are detected, a separate
process model can be discovered between each pair of points to help us understand the evolving
of processes.
        </p>
        <p>
          Some research also focuses on detecting other complex behaviours. For example, Lu et al.
[24] propose a method to handle duplicate activities in event logs. More specifically, the same
activity may execute in diferent stages of a process. A more comprehensive process model
can be discovered if we split such an activity into multiple activities. Dees et al. [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] propose a
method to visualise the behaviours of context activities on the edges of process models (i.e.,
activities which can happen at anytime during the execution of the process). Dubinsky et al.
[25] propose a method to detect the ”split-cases” behaviours in event logs (i.e., when a case is
illegally split into multiple cases).
        </p>
        <p>In a nutshell, stand-alone tools are independent from process discovery algorithms. They can
discover more insights about the process from event logs which usually cannot be discovered
directly by process discovery algorithms. These methods can be used together with process
discovery algorithms to enhance our understanding of business processes described in event
logs.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Research Approach</title>
      <p>Our research approach is adapted from the Design Science Research (DSR) [26] methodology.
Our research contains the following stages:
• Identifying Problems: At this stage, literature review is conducted. The literature review
focuses on research related to detecting process behaviours from event logs (eg., process
discovery algorithms, concept drift detection algorithms, trace clustering algorithms,
etc.). Based on the literature review, gaps can be identified among existing literature (eg.,
existing concept drift detection algorithms cannot distinguish process drifts from noises).
• Designing and Developing Solutions: Once a gap has been identified among existing
literature, a solution can then be proposed to solve the problem. Then a software can be
built to implement the proposed solution. Existing open-source software packages can be
modified for faster development process.
• Demonstration and Evaluation: When a potential solution is implemented, evaluation
should be conducted to show the capabilities of the proposed solution. The evaluation
usually contains two parts: firstly, the method is evaluated empirically using a big number
of synthetic datasets. The performance of the proposed method can also be compared
with existing methods. Secondly, the method is evaluated using real-life datasets.
• Communication: If a valid solution is built, the work can be presented to the research
community through academic conferences, workshops or journals.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Current Results</title>
      <p>In this section, we briefly introduce some of our work to discover complex process behaviours
in event logs. Please refer to the corresponding references for the details of our proposed
methods and evaluation results. It has to be noted that all work presented in this section has
been evaluated using publicly available datasets. The implementations of these methods are
also publicly available.</p>
      <sec id="sec-4-1">
        <title>4.1. Discovering Switch Behaviours in Process Mining</title>
        <p>In [17], we propose a novel method to extend the inductive miner to discover switch behaviours.
Assume there is an exclusive decision choice in a process model, and the decision point is
split into multiple branches. In real-life event logs, it is possible to switch between diferent
branches after the decision has been made. However, due to the limitation of process trees, the
original inductive miner is unable to discover such behaviours. A ”follower model” with very
low precision can be returned when such behaviours exist in event logs.</p>
        <p>To solve the problem, we firstly extend the process tree notation to allow the presentation of
switch behaviours. The new notation is called ”switch process tree”. Each switch process tree
can be translated into an equivalent workflow net. In addition, with some constraints of switch
process trees, their corresponding workflow nets can be guaranteed to be sound. Fig. 1 shows
an example process tree and its corresponding workflow net.</p>
        <p>The extension of process trees allows us to extend the inductive miner to discover switch
behaviours. As shown in Table 1, when switch behaviours exist in event logs, our proposed
method can significantly improve the precision of the discovered process models. The discovered
process models by the extended inductive miner can accurately present the process behaviours
in event logs.</p>
        <p>Finally, the method is also evaluated using a real-life dataset (”BPIC13-incident” event log
from the ”4TU Center for Research Data”). As shown in Table 2, a more accurate and simpler
process model is discovered by our proposed method.</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Discovering Concept Drifts in Process Mining</title>
        <p>In [21], we propose a method to accurately detect time points of process drifts in event logs. A
process drift point is defined as the time point when there is a statistically significant diference
among the observed process behaviours before and after the change point. Most existing process
drift detection algorithms assume the input event logs to be clean and cannot diferentiate
process drifts from noises. Our proposed method can not only accurately detect process drift
points, but can also be robust to noises. Evaluation results show that our proposed method
can consistently perform better than existing methods. Fig. 2 shows the evaluation results
comparing to the baseline [22] when 20% of noises are inserted into the event logs.</p>
        <p>In [28], we propose a method to detect branching frequency changes in process models.
Branching frequency changes refer to changes in frequencies between diferent options when
there is an exclusive choice. Our method is evaluated using a publicly available event log
(”Italian Help Desk” event log from the ”4TU Center for Research Data”). The process model is
presented in Fig. 3 and the results are presented in Fig. 4. Two frequency changes are detected
in the event log, and the frequencies between choosing activity ”Wait”, ”Require upgrade” and
”Resolve ticket” after ”Take in charge ticket” change significantly after each drift point.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusions and Future Work</title>
      <p>In this paper, we explain the need for developing new techniques to discover complex behaviours
in event logs for better understanding of business processes. On the one hand, existing process
discovery algorithms can be extended to handle complex behaviours. On the other hand,
stand-alone tools can also be constructed for the detection of specific types of behaviours.</p>
      <p>Although we have provided some solutions for the research problem, there are still some
challenges. Firstly, there is the lack of methods to validate the results. For example, in [17],
although a process model with higher precision value can be obtained from the publicly available
event log, it may still be insuficient to conclude that switch behaviours actually exist in the
process. We plan to evaluate this work empirically to evaluate its capabilities in the future.
Secondly, some methods heavily rely on user-defined parameters. For example, In [ 21], a window
size is required from users. The window size defines the number of events in each sample when
performing statistical tests. Diferent process drift points can be reported with diferent window
sizes. In [28], the detection of drift points relies on an external change detection algorithm. The
detection results are dependent on the parameters of the external algorithm.</p>
      <p>Finally, we also plan to develop methods to discover other complex behaviours such as the
automatic detection of cancellation behaviours and non-free-choice behaviours in event logs.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>This research project is supervised by Associate Professor Simon K. Poon from the School of
Computer Science, the University of Sydney.
Springer International Publishing, Cham, 2017, pp. 93–113.
[17] Y. Lu, Q. Chen, S. Poon, A novel approach to discover switch behaviours in process mining,
in: S. Leemans, H. Leopold (Eds.), Process Mining Workshops, Springer International
Publishing, Cham, 2021, pp. 57–68.
[18] M. Leemans, W. M. Van Der Aalst, M. G. Van Den Brand, Recursion aware modeling and
discovery for hierarchical software event log analysis, in: 2018 IEEE 25th international
conference on software analysis, evolution and reengineering (SANER), IEEE, 2018, pp.
185–196.
[19] X. Lu, A. Gal, H. A. Reijers, Discovering hierarchical processes using flexible activity trees
for event abstraction, in: 2020 2nd International Conference on Process Mining (ICPM),
2020, pp. 145–152. doi:1 0 . 1 1 0 9 / I C P M 4 9 6 8 1 . 2 0 2 0 . 0 0 0 3 0 .
[20] S. J. Leemans, K. Goel, S. J. van Zelst, Using multi-level information in hierarchical
process mining: Balancing behavioural quality and model complexity, in: 2020 2nd
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I C P M 4 9 6 8 1 . 2 0 2 0 . 0 0 0 2 9 .
[21] Y. Lu, Q. Chen, S. Poon, A robust and accurate approach to detect process drifts from event
streams, in: A. Polyvyanyy, M. T. Wynn, A. Van Looy, M. Reichert (Eds.), Business Process
Management, Springer International Publishing, Cham, 2021, pp. 383–399.
[22] A. Ostovar, A. Maaradji, M. La Rosa, A. H. M. ter Hofstede, B. F. V. van Dongen,
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[23] A. Yeshchenko, C. Di Ciccio, J. Mendling, A. Polyvyanyy, Visual drift detection for sequence
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