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Discovering Hierarchical Processes Using Flexible Activity Trees for Event Abstraction

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Abstract

Processes, such as patient pathways, can be very complex, comprising of hundreds of activities and dozens of interleaved subprocesses. While existing process discovery algorithms have proven to construct models of high quality on clean logs of structured processes, it still remains a challenge when the algorithms are being applied to logs of complex processes. The creation of a multi-level, hierarchical representation of a process can help to manage this complexity. However, current approaches that pursue this idea suffer from a variety of weaknesses. In particular, they do not deal well with interleaving subprocesses. In this paper, we propose FlexHMiner, a three-step approach to discover processes with multi-level interleaved subprocesses. We implemented FlexHMiner in the open source Process Mining toolkit ProM. We used seven real-life logs to compare the qualities of hierarchical models discovered using domain knowledge, random clustering, and flat approaches. Our results indicate that the hierarchical process models that the FlexHMiner generates compare favorably to approaches that do not exploit hierarchy.
Discovering Hierarchical Processes
Using Flexible Activity Trees for Event Abstraction
Xixi Lu, Avigdor Gal, and Hajo A. Reijers
Dept. of Information and Computing Sciences
Utrecht University, Utrecht, The Netherlands
x.lu@uu.nl, h.a.reijers@uu.nl
Faculty of Industrial Engineering and Management
Technion – Israel Institute of Technology, Haifa, Israel
avigal@technion.ac.il
Abstract—Processes, such as patient pathways, can be very
complex, comprising of hundreds of activities and dozens of
interleaved subprocesses. While existing process discovery algo-
rithms have proven to construct models of high quality on clean
logs of structured processes, it still remains a challenge when
the algorithms are being applied to logs of complex processes.
The creation of a multi-level, hierarchical representation of a
process can help to manage this complexity. However, current
approaches that pursue this idea suffer from a variety of
weaknesses. In particular, they do not deal well with interleaving
subprocesses. In this paper, we propose FlexHMiner, a three-
step approach to discover processes with multi-level interleaved
subprocesses. We implemented FlexHMiner in the open source
Process Mining toolkit ProM. We used seven real-life logs to
compare the qualities of hierarchical models discovered using
domain knowledge, random clustering, and flat approaches. Our
results indicate that the hierarchical process models that the
FlexHMiner generates compare favorably to approaches that do
not exploit hierarchy.
Index Terms—Automated Process Discovery; Process Mining;
Event Abstraction; Model Abstraction; Hierarchical Process
Discovery
I. INTRODUCTION
Complex processes often comprise of hundreds of activities
and dozens of subprocesses that run in parallel [1], [2]. For
example, in healthcare, a patient follows a certain process that
consists of several procedures (e.g., lab test and surgery) for
treating a medical condition. Studies have shown qualitatively
that using hierarchical process models to represent complex
processes can improve understandability and simplicity by
“hiding less relevant information” [3]. In particular, the use
of modularized, hierarchical process models, where process
activities are collected into subprocesses, can be presented in
a condensed higher-level presentation, revealing more details
upon request.
Process discovery, a prominent task of process mining, aims
at automatically constructing a process model from an event
log. Over the years, dozens of discovery algorithms have been
proposed [4]–[7]. These have proven to perform very well on
relatively clean logs of structured processes. However, given
the complexity of real-life processes, these algorithms tend to
discover overfitted or overgeneralized models that are difficult
to comprehend [8]. Existing discovery algorithms tend to
disregard any hierarchical decomposition, whereas discovering
hierarchical process models may help decrease the complexity
of the discovery task.
Few hierarchical process discovery algorithms have been
proposed [9]–[14]. While some approaches, such as [12], aim
to automatically detect subprocesses, these algorithms are rigid
in their assumptions and require extensive knowledge encoding
for every event in the log regarding the causalities between the
activities. Other approaches assume that subprocesses do not
interleave [9], [14], which lead to discovering inaccurately,
overly segmented models (see Fig. 1). It is also unclear how
these approaches compare to conventional, flat models in terms
of quality measures such as fitness and precision.
In this work, we propose FlexHMiner (FH), a three-step
approach for the discovery of hierarchal models. We formalize
the concept of activity tree and event abstraction, which allows
us to be flexible in the ways of computing the process hierar-
chy. We illustrate this flexibility by proposing three different
techniques to discover an activity tree: (1) a fully domain-
based approach (DK-FH), (2) a random approach (RC-FH),
and (3) a fall-back, flat activity tree (F-FH). After obtaining
an activity tree, the second step of our approach is to compute
the logs for each subprocess using log abstraction and log
projection. Finally, FlexHMiner discovers a subprocess model
for each subprocess by leveraging the capabilities of existing
discovery algorithms. Using the domain-based approach as
the gold standard and the flat tree approach as base line, we
compare the three ways of discovering an activity tree using
seven real-life logs.
The main contribution of this work is a novel approach to
discover hierarchical process models from event logs, which
(1) can handle multi-level interleaving subprocesses and (2)
is flexible in its data requirements so that it can adapt to
the situations when there is domain knowledge and when
there is not. We evaluated FlexHMiner using seven real-life,
benchmark event logs1.
In the remainder, we define the research problem in Sect. II.
The proposed approach is described in Sect. III. The evaluation
1The source code and the results can be found at: github.com/xxlu/prom-FlexHMiner
arXiv:2010.08302v1 [cs.DB] 16 Oct 2020
(a) The sequential subprocessses
discovered by SCM [14].
(b) The interleaving subprocesses
discovered by our DK-FH.
Fig. 1: Difference in the discovered root models for the
BPIC2012 log.
TABLE I: An example of an event log of a healthcare process.
EPatient Description Subprocess Act Timestamp
e1101 Visit Contact C Vi 10-10-2019
e2101 Calcium Labtest L Ca 11-10-2019
e3101 Register Contact C Re 12-10-2019
e4101 Glucose Labtest L Gl 13-10-2019
e5101 Consultation Contact C Cs 14-10-2019
e6101 Consultation Contact C Cs 15-10-2019
e7102 Register Contact C Re 16-10-2019
e8102 Glucose Labtest L Gl 17-10-2019
... ... ... ... ... ...
results are presented in Sect. IV. Sect. V discusses related
work, and Sect. VI concludes the paper .
II. ACTIVITY TRE E AN D PROCESS HIERARCHY
Preliminaries: Let σ=ha1,· · · , ani ∈ Σbe a sequence
of activities, which is also called a trace. Let a multiset
LB)of traces be an event log. Tab. I shows a
list of events; Fig. 2(a) shows the sequential traces, in a
graphical representation, where each square represents an
event that is labeled with an activity. Given an event log,
a process discovery algorithm Dautomatically constructs a
process M(e.g., in Petri net notation). The quality of such
a model Mcan assessed with respect to the log Lusing
four quality dimensions: fitness, precision, generalization, and
complexity [8].
To discover a hierarchical process model, we leverage a
rather known concept that represents the process hierarchical
information and call it activity tree. We define an activity tree
as the hierarchical relations between activities of a process.
Formally, an activity tree is a non-overlapping, hierarchical
clustering of activities.
Definition 1 (Activity tree).Let Σbe a set of activities and
Lan event log over Σ. Let Abe a superset of Σ, i.e., ΣA.
Function γ:A→ P(A)is a mapping that maps each activity
xAto a set of activities XAas the children of x. An
activity tree (A, γ)is valid for L, if and only if:
1) The children of any two labels do not overlap, i.e., for
each x, y A,x6=yγ(x)γ(y) = .
2) The union of the leaves is Σ, i.e., the set of activities that
occurred in log L, i.e., {xA|γ(x) = ∅} = Σ.
3) The tree (A, γ )is connected, i.e., for each xA, either
there is yAsuch that xγ(y), or xis the root.
Note that constraints (2) and (3) imply that for all xA,
x /γ(x). Furthermore, it is also possible to define an activity
tree as a directed acyclic graph where each node represents
an activity and has only one incoming edge, except the root
node, which does not have any incoming edge.
Example 1. Fig. 2(b) exemplifies the activity tree (A, γ),
where A={root,C,L,S,Vi,Cs,Re,Ca,Gl,Cr,Or,
Pr,Op}, and, for example, γ(C) = {Vi,Cs,Re}.
We call the node that has no parent in γthe root node, and
the corresponding process the root process. For each aA,
γ(a)6=, we call it a (sub)process awith γ(a)as its activities.
We define the height of a node in the activity tree, which is
later used to recursively compute the abstracted logs bottom-
up. Let height :AN0be a function that maps each xA
to the height (a non-negative integer) of xin the activity tree
(A, γ). For each xA, if γ(x) = , then height(x) = 0,
else height(x) = 1 + Max cγ(x)height(c). A process model
with a maximal height of an activity tree is 1, is called flat.
III. THE FL EX HMIN ER ALGORITHM
In this section, we discuss the three steps of the FlexHMiner
approach: (1) compute an activity tree, (2) compute abstracted
logs, and (3) compute subprocess models.
A. Computing Activity Tree
For the first step, computing an activity tree, we present
three different methods: one supervised using domain knowl-
edge, one automated using random clustering, and one fall-
back using flat tree.
1) Using Domain Knowledge: Domain knowledge can be
used, as a gold standard, to create an activity tree. This can
be done manually. In other situations, the log itself may
already contain an encoding of human knowledge that can
be utilized in creating the activity tree. In Tab. I, the column
Act demonstrates such an encoding of hierarchy. For instance,
the activity label C_Vi, indicating that the event belongs to
subprocess C. Following the same strategy as the State Chart
(a) Log L1 of three traces
CsVi Ca GlRe Cs
CaRe Gl OrVi Pr Op
Cs Cr
Gl
Re Cr OrVi Pr Op
Cs Cs
(b) Activity tree (𝐴, 𝛾)
CaCs GlReVi
Root
CL
Cr
S
Or Pr Op
CsCa Gl Ce
CaCsGl Or Pr Op
CeCr
Gl
CsCr Or Pr OpCe
CsLsLeCe
CsLsOr Pr Op
CeLe
Le
CsLsOr Pr OpCe
σ1
σ2
σ3
CsLsLeCe
CsLsSsSe
CeLe
Le
CsLsSsSe
Ce
c𝐿2
d𝐿3
e𝐿4
σ’1
σ’2
σ’3
σ’’1
σ’’2
σ’’3
σ’’’1
σ’’’2
σ’’’3
𝐴𝐿 ← 𝑓
(𝐿1, “C”)
𝐴𝐿 ← 𝑓
(𝐿2, “L”)
𝐴𝐿 ← 𝑓
(𝐿3, “S”)
(f) The Root process
CS
LS
CE
LE
SSSE
Fig. 2: FlexHMiner applied on the running example.
Miner (SCM) [14], a simple text parser is built to split the
labels of activities and to convert the domain knowledge into
an activity tree. For our experiment, we found seven real-life
logs of two processes, where such information regarding the
hierarchy is readily encoded in the activity labels 2 3.
2) Using Random Clustering: Let LB)be an event
log. Let maxSize 2be the indicated maximal size of
subprocesses. The random clustering algorithm, as listed in
Algorithm 1, takes Σand maxSize as inputs and creates ran-
dom subprocesses of size less than maxSize. It first initializes
the activity tree (A, γ)using Σ(see Line 1). It then uses
maxSize to determine the number nof subprocesses at the
current height (see Line 2-5). Next, it creates nparent nodes as
Pand simply assigns each activity cCrandomly to a cluster
pP(see Line 6-12), while updating Aand γaccordingly
(see Line 8 and 11). To decide whether to continue with the
next height, the current set of parent nodes Pbecomes the set
of child nodes C(see Line 13): if the size of C(i.e., |C|) is
greater than maxSize, then the algorithm creates another level
of parent nodes (as abstracted processes); otherwise, the while
loop terminates, and the root node is added (see Line 15 and
16). In this paper, maxSize is set to 10 as default. We use
the random clustering to show an unsupervised way to create
an activity tree and to investigate a possible baseline for the
qualities of hierarchical models.
3) Using Flat Tree: Given a log Lover activities Σ, a flat
activity tree (A, γ)(with height 1) is constructed as follows.
2See the description of the BPI Challenge 2012 at https://www.win.tue.
nl/bpi/doku.php?id=2012:challenge: “The event log is a merger of three
intertwined sub processes. The first letter of each task name identifies from
which sub process (source) it originated.
3See the description of the BPI Challenge 2015 at https://doi.org/10.
4121/uuid:31a308ef-c844- 48da-948c- 305d167a0ec1.: “The first two digits as
well as the characters [of the activity label] indicate the subprocess the
activity belongs to. For instance ... 01_BB_xxx indicates the ‘objections
and complaints’ (‘Beroep en Bezwaar’ in Dutch) subprocess.
We have A= Σ ∪ {root}. For all aΣ,γ(a) = ; and for
root A,γ(root)=Σ. We use the flat tree approach as a
fall-back.
B. Computing Abstracted Logs and Models
Given an activity tree (A, γ)and a log L, the second
step uses the projection (f) and abstraction (f) functions
to recursively compute sublogs for each non-leaf node in the
tree. We first discuss the projection and abstraction functions,
after which we present the algorithm.
1) Projection: Given a log L, an activity tree (A, γ), and
a subprocess sp A, the projection of Lon the activities
γ(sp)of sp is rather straightforward and standard, which
allows us to create a corresponding log for sp. The projection
function simply retains the events of activities γ(sp)and
remove the rest. Formally, given a trace σ=hei · σ0: if
eγ(sp),f(σ, sp) = hei · f(σ0, sp), otherwise, f(σ, sp) =
hi · f(σ0, sp). We overload the function for any log L:
f(L, sp) = SσLf(σ, sp), if f(σ, sp)6=hi.
Example 2. For example, given the (simplified) trace σ1=
hVi,Ca,Re,Gl,Cs,Csi, the subprocess C, and the activity-
hierarchy γwhere γ(C) = {Vi,Cs,Re}(as shown in Fig. 2(a)
and (b)) then the trace of Cis computed as f(σ1,C) =
hVi,Re,Cs,Csi.
2) Abstraction: The abstraction function freturns the
abstracted, intermediate log after abstracting (removing) the
internal behavior of a subprocess sp. Essentially, the abstrac-
tion function hides irrelevant internal behavior by not retaining
the detailed events of a subprocess; it only keeps the relevant
behavior. In this paper, we consider both the start and the
end events of a subprocess as the relevant behavior. In this
way, the abstracted log only records when a subprocess starts
and ends4. If a subprocess xhas different start activities (e.g.,
Vi and Re), they are abstracted into a single start activity xs
4Note that other abstraction functions can be conceived, e.g., a function that will only
render the start or the end event of the subprocess.
Algorithm 1 Compute random tree (A, γ)
Input: the input log Lover Σ, and the maximal size of a process maxSize
Output: activity tree (A, γ),
1: AΣ; and for aΣdo γ(a)← ∅ {initiate Aand the leaves of γ}
2: CΣ{Use Cto represent the child activities at the current height}
3: while |C|>maxSize do
4: {create parent clusters Pto ensure the size of a process is at most maxSize,
and apply clustering to assign each cCto a parent cluster p}
5: n← b(|C| −1)/maxSizec+ 1 {Calculate the number of parents}
6: Create labels p1,··· , pn{Create nrandom parent nodes/processes}
7: Initiate P← {p1,··· , pn}:for pPdo γ(p)← ∅
8: AAP
9: for cCdo
10: Select a random pP, where |γ(p)|<maxSize
11: γ(p)γ(p)∪ {c}
12: end for {all children have been assigned to a parent process}
13: CP
14: end while {| C|≤ maxSize}
15: AA∪ {root}{Create the root node/process and add to A}
16: for cCdo γ(root)γ(root) {c}{Assign cCto the root process}
17: return (A, γ)
(e.g., Cs, see Fig. 2(c)). The same holds for the end activities,
which are abstracted into a single end activity xe.
Let SP =γ(sp)denote the set of activities of subprocess
sp. Let Isdenote the index of the first event of sp in σas
Is= mineσeSP σ[e]. Similarly, we use Ieto refer to the
index of the last event of sp in σ, i.e., Ie= maxeσeSP σ[e].
We define fas follows:
f(σ, SP) =
hei · f(σ0,SP)e /SP
hspsi · f(σ0,SP)eSP , σ[e] = Is
hspei · f(σ0,SP)eSP , σ[e] = Ie
hi · f(σ0,SP)eSP
Is< σ[e]< Ie
(1)
We overload the function for any log L, i.e., f(L, sp) =
SσLf(σ, sp)5.
Example 3. For example, after abstracting subprocess C
from σ1, we have f(σ1,C) = hCs,Ca,Gl,Cei. Similar,
the trace after abstracting subprocess Lis f(σ1,L) =
hVi,Ls,Re,Le,Cs,Csi. To obtain the parent-trace, we
apply frecursively; for instance, f(f(σ1,C),L) =
f(f(σ1,L),C) = hCs,Ls,Le,Cei=σ00
1, see Fig. 2(d).
The abstraction function fis commutative and associative
for non-related subprocesses6. These two properties allow
Algorithm 2 to use the abstraction function in a recursive,
bottom-up manner and to go iteratively through the nodes.
The algorithm creates an abstracted log at each height of the
activity tree, which is discussed in the next section.
3) Recursion: The algorithm computes the log mapping α
and the model mapping βwith three inputs: (1) an event log
L, (2) an activity tree (A, γ), and (3) a flat process discovery
algorithm D. It applies the projection function bottom-up
for each subprocess on the abstracted log AL, starting with
height 1 until but does not include the root process (see Lines
2 - 13). For every subprocess pPof the same height, the
algorithm applies the projection function to obtain the sublog
Lpfor p(Line 8) and updates the log mapping and model
mapping (see Lines 9 and 10). The algorithm then computes
the intermediate, abstracted log AL by using the abstraction
function f(see Line 11). The abstracted log AL is updated
after each pP(see Lines 5 - 12) at height i. The algorithm
terminates once it has completed processing the root process.
It returns a hierarchical model (A, γ, α, β), where the log
mapping αmaps each (sub)process pA,γ(p)6=, to the
associated log Lp, and the model mapping βmaps each pto
the associated model Mp=D(Lp)of (sub)process p.
Example 4. Given the log L1and activity tree (A, γ)),
respectively, shown in Fig. 2(a) and (b), the three subprocesses
C,L, and Shave height 1. Fig. 2(c), (d), and (e) show the
abstracted log AL obtained after each iteration of the inner-
loop at Lines 5-11. For example, in the first iteration (see Fig. 2
(c)), applying f(L1,C)on log L1, we obtain AL =L2where
5For the sake of brevity, we consider the labels a=as=aefor both projection and
abstraction functions and only distinguish them when we apply a discovery algorithm.
6Two nodes are non-related if they do not share ancestors or descendants in the activity
tree)
TABLE II: Statistical information of the event logs.
Data #acts #evts #case #dpi avg e/c max e/c
BPIC12 * 36 262,200 13,087 4,366 20 175
BPIC17f * 18 337,995 21,861 1,024 18 32
BPIC15 1f * 70 21,656 902 295 24 50
BPIC15 2f * 82 24,678 681 420 36 63
BPIC15 3f * 62 43,786 1,369 826 32 54
BPIC15 4f * 65 29,403 860 451 34 54
BPIC15 5f * 74 30,030 975 446 31 61
the activities of Cis removed from L2and only the start and
the end of Care retained (as discussed in Example 3). In
the second iteration, the algorithm continues with log AL and
applies f(AL, L), see Fig. 2 (d).
IV. EMPIRICAL EVALUATION
We implemented the FlexHMiner approach in the process
mining toolkit ProM7. We evaluated the quality of the models
created by FlexHMiner using seven real-life data sets and
compared the results.
In the following, we discuss the data sets and the experimen-
tal setup, followed by our empirical analysis. All experiments
are run on an Intel Core i7- 8550U 1.80GHZ with a processing
unit of a 16 GB HP-Elitebook running Windows 10 Enterprise.
A. Data sets
An overview of the statistical information, including the
number of distinct activities (acts), events (evts), cases, distinct
sequences (dpi), and of events per case (e/c) of the seven logs,
is given in Tab. II. These logs are the filtered logs used in [8]
as a benchmark8, which allows us to compare our result with
the qualities of the flat models reported in [8].
7http://www.promtools.org/. The source code and results: github.com/xxlu/prom-
FlexHMiner
8https://doi.org/10.4121/uuid:adc42403-9a38- 48dc-9f0a- a0a49bfb6371
Algorithm 2 Compute log hierarchy αand models β
Input: Log L, activity tree (A, γ), and discovery algorithm D
Output: Log mapping αand model mapping β
1: maxHeight Max cAheightγ(c){calculate the maximal height of the
tree}
2: AL L
3: for i= 1 to maxHeight 1do
4: P← {pA|height(p) = i}
5: for pPdo
6: {Iteratively go through each pPat the same height iand perform log
projection and abstraction}
7: Cγ(p){get the activities Cof subprocess p}
8: Lpf(AL, C){project the log so far on the activities C}
9: α(p)Lp
10: β(p)D(Lp)
11: AL f(AL, p){abstract the log so far using the activities C}
12: end for {the log so far AL has been abstracted from Pto height i}
13: end for {i== maxHeight}
14: α(root)AL {map the root to the resulted abstracted log}
15: β(root)D(AL){map the root to the discoverede model}
16: return (A, γ, α, β)
B. Experimental Setups
For computing activity tree, we used the three methods:
random (RC-FH), flat tree (F-FH), and domain knowledge
(DK-FH). For computing hierarchical models, we use two
state-of-the-art process discovery algorithms as D, namely the
Inductive Miner with 0.2 path filtering (IMf) and the Split
Miner (SM) [7] with standard parameter settings. According
to the recent work of Augusto et al. [8], these two algorithms
outperform others in terms of the four quality measures and
execution time.
We run these six configurations on the seven data sets. For
each log and for each of the two flat discovery algorithms, we
also report the results in [8], for which we use F* to represent.
Thus, in total eight rows for each data set.
C. Model Quality Measures
We assess the quality of a model M, with respect to a log
L, using the following four dimensions:
For fitness (L, M )[0,1], we use the alignment based
fitness defined by Adriansyah et al. [15], also used in [8].
For precision (pr(L, M )[0,1]), we use the measure
defined in [16], known as ETC-align.
We also compute the F1-score, which is the har-
monic mean of fitness and precision: f1(M, L)=2
(L,M)pr (L,M )
(L,M)+pr (L,M ).
For generalization, we follow again the same approach
adopted in [8]. We divide the log into k= 3 subsets:
Lis randomly divided into L1,L2,L3,ge(L, M ) =
1
3P1i32fi(Li,Mi)pr(L,Mi)
fi(Li,Mi)+pr(L,Mi)where Micorresponds
to Li.
Finally, for complexity, we report the size (number of
nodes) and the Control-Flow Complexity (CFC) of a
model [8]. Let P N = (P, T , F, l, mi, mf)be a Petri
Net. Size(P N ) =|P|+|T|.
CFC (P N) = X
tT(|t|>1∨|t|>1)
1 + X
pP(|p|>1∨|p|>1)
|p|
Let (A, γ, α, β )be a hierarchical model returned. Let
q∈ {,pr,F1 ,Ge,CFC ,Size}be any quality measure that
takes a model Mand/or a log Las inputs and returns
the quality value of the model. We calculate and report
the average quality measure qas follows : q(A, γ, α, β) =
avgaAγ(a)6=q(β(a), α(a)). For example, (A, γ, α, β)is
calculated as the average value of the individual fitness values
of each subprocess in the hierarchical model.
The computation of fitness, precision, and generalization
uses a state-of-the-art technique known as alignment [15]9. As
mentioned, we also list the quality values reported by Augusto
et al. using “F*” [8]. Since we were unable to compute all
qualities of the flat models, and for the sake of consistency,
we mainly discuss our results with respect to the results of
“F*”.
9A 60 minute time-out limit is set for computing the alignment of each
model. When the particular quality measurement could not be obtained due
to either syntactical or behavioral issues in the discovered model or a timeout
when computing the quality measures, we record it using the “” symbol.
TABLE III: Evaluation results of models for the seven logs.
Data CAlg DAlg F i P r F 1Ge C F C S ize #SPs #Act
BPIC12
F-FH
IMf
- - - - 66 115 1 24
F* 0.98 0.50 0.66 0.66 37 59 1 -
DK-FH 0.96 0.78 0.86 0.85 20 36 4 8
RC-FH 0.97 0.78 0.86 0.88 20 35 4 8
F-FH
SM
0.97 0.55 0.70 0.69 53 89 1 24
F* 0.75 0.76 0.75 0.76 32 53 1 -
DK-FH 0.89 0.94 0.91 0.91 10 22 4 8
RC-FH 0.92 0.90 0.90 0.90 14 28 3 8
BPIC17f
F-FH
IMf
0.98 0.57 0.72 0.73 20 51 1 18
F* 0.98 0.70 0.82 0.82 20 35 1 -
DK-FH 0.97 0.98 0.97 0.97 6 17 4 6
RC-FH 0.98 0.90 0.94 0.92 9 22 3 7
F-FH
SM
0.98 0.63 0.76 0.76 23 47 1 18
F* 0.95 0.85 0.90 0.90 17 32 1 -
DK-FH 0.96 0.98 0.97 0.97 6 18 4 6
RC-FH 0.98 0.92 0.95 0.95 8 20 3 7
BPIC15 1f
F-FH
IMf
0.96 0.36 0.52 0.51 128 217 1 70
F* 0.97 0.57 0.72 0.72 108 164 1 -
DK-FH 0.99 0.87 0.91 0.93 9 19 15 6
RC-FH 0.97 0.84 0.88 0.88 16 29 9 10
F-FH
SM
0.93 0.87 0.90 0.90 64 152 1 70
F* 0.90 0.88 0.89 0.89 43 110 1 -
DK-FH 0.96 0.98 0.97 0.97 4 14 15 6
RC-FH 0.88 0.99 0.93 0.93 8 22 9 10
BPIC15 2f
F-FH
IMf
- - - - 183 313 1 82
F* 0.93 0.56 0.70 0.70 123 193 1 -
DK-FH 0.97 0.91 0.93 0.93 7 16 21 5
RC-FH 0.95 0.85 0.89 0.88 16 33 10 10
F-FH
SM
0.83 0.88 0.85 0.85 72 198 1 82
F* 0.77 0.90 0.83 0.82 41 122 1 -
DK-FH 0.94 0.99 0.97 0.97 4 13 21 5
RC-FH 0.83 0.96 0.89 0.89 11 26 10 10
BPIC15 3f
F-FH
IMf
- - - - 136 244 1 62
F* 0.95 0.55 0.70 0.69 108 159 1 -
DK-FH 0.97 0.94 0.95 0.95 6 15 17 5
RC-FH 0.94 0.87 0.90 0.89 16 33 8 10
F-FH
SM
0.81 0.92 0.86 0.87 50 135 1 62
F* 0.78 0.94 0.85 0.85 29 90 1 -
DK-FH 0.95 0.99 0.97 0.97 3 12 17 5
RC-FH 0.87 0.98 0.92 0.92 10 23 7 9
BPIC15 4f
F-FH
IMf
- - - - 121 242 1 65
F* 0.96 0.58 0.72 0.72 111 162 1 -
DK-FH 0.98 0.96 0.97 0.97 5 13 21 4
RC-FH 0.97 0.81 0.87 0.87 18 35 8 10
F-FH
SM
0.79 0.92 0.85 0.85 51 147 1 65
F* 0.73 0.91 0.81 0.80 31 96 1 -
DK-FH 0.95 0.99 0.97 0.97 2 11 21 4
RC-FH 0.83 0.98 0.90 0.89 8 24 8 10
BPIC15 5f
F-FH
IMf
- - - - 142 255 1 74
F* 0.94 0.18 0.30 0.61 95 134 1 -
DK-FH 0.98 0.95 0.97 0.96 5 14 21 5
RC-FH 0.98 0.80 0.87 0.87 19 34 9 10
F-FH
SM
0.85 0.91 0.88 0.88 54 163 1 74
F* 0.79 0.94 0.86 0.85 30 102 1 -
DK-FH 0.96 1.00 0.98 0.98 2 11 20 5
RC-FH 0.83 0.98 0.90 0.90 8 23 9 10
On the seven starred data sets, there are two subprocesses
for RC-FH-SM, one for DK-FH-SM, and none for DK-FH-
IMf and RC-FH-IMf, where the returned alignments were
indicated unreliable. As a result, the fitness of these models are
-1, and subsequently, the precision and generalization cannot
be computed. The results of these models are excluded when
computing the average quality scores.
D. Results and Discussion
Tab. III summarises the results of our evaluation. For each
data set (Data) and each of the two discovery algorithms
(DAlg), we obtained four (hierarhical) models and report on
the results. To also provide concrete examples, Fig. 3(a)
shows the root process and three subprocesses obtained by
applying DK-FH-IMf on the BPIC15 1f log, while the other
subprocesses are hidden (abstracted). By contrast, Fig. 3(b)
shows the flat model by F-FH-IMf on the same log.
Fitness. Column F i (Tab. III) reports on the average fitness
of the models discovered. For both IMf and SM, in 5 of
the seven logs, the hierarchical models returned by DK-FH
achieved a better fitness score than F*. More specifically,
there is on average an increase of 0.015 (2%) in fitness,
when compared the fitness of F* to DK-FH. Considering SM,
the improvement in fitness is more significant: the average
increase in fitness is 17%, from 0.810 to 0.946. The moderate
improvement in fitness for IMf is due to the fact that IMf
tends to optimize fitness. As the average fitness of the seven
models is already very high (0.959), there is little room for
improvement.
Precision. Column P r (Tab. III) lists the average precision
of the models. When comparing the average precision scores
of the subprocesses (DK-FH) to the flat models (F*), DK-
FH has achieved a considerable improvement in precision,
especially for IMf. For all seven logs, the subprocesses ob-
tained by both DK-FH-IMf and DK-FH-SM have achieved an
average precision higher than the F* approaches: for DK-FH-
IMf, the average precision is increased by 75.4% (from 0.520
to 0.912); for DK-FH-SM, there is also an 11.2% increase in
the precision scores (from 0.883 to 0.982).
An explanation for such significant improvements in the
average precision can be the following. As the subprocesses
are relatively small and the sublogs do not contain interleaved
behavior of other concurrent subprocesses, it allowed the dis-
covery algorithm to discover rather sequential models of high
precision, while maintaining the high fitness (see Fig. 3 (b), (c)
and (e)). When a subprocess itself contains much concurrent
behavior (for example, see Fig. 3 (d)), the highly concurrent,
flexible behavior is then localized within this one subprocess,
without affecting the models of other subprocesses.
F1 score. For both IMf and SM and for all seven logs, the
average F1 scores of the subprocesses of DK-FH outperform
the ones of F*. This is mainly due to the improvement in both
fitness (for SM) and precision (for IMf), which led to the
increase in the harmonic mean of fitness and precision. On
average DK-FH achieved an increase of 41.9% (from 0.660
to 0.936) for IMf and 14.4% for SM (from 0.842 to 0.962) in
the F1 scores over the seven logs.
Fig. 5 shows the distribution of the F1-scores of the models
of each approach in more detail (IMf on the left and SM on
the right). Compared to the F1 scores of the models by F-
FH (see purple lines), DK-FH (blue boxplot and dots) always
scores higher. Compared to the F* results, there are only three
exceptional cases for IMf. We looked into these models of IMf
and found that many activities are put in parallel. Thus, fitness
was very high (e.g., 0.972) but precision was very low (e.g.,
0.335). Interestingly, for the exact same subprocess, SM was
able to discover a much more sequential model. This model
still has a high fitness (0.958) but a much higher precision
(1.00) and also a high generalization (0.979). This can be an
interesting future work: since DK-FH allows for the use of any
discovery algorithm, one can design an algorithm that selects
the best algorithm (model) for each subprocess to further
increase the quality of the hierarchical models.
Generalization. Column Ge (Tab. III) reports on the gen-
eralization scores (using 3-fold cross validation). In all seven
logs, for both IMf and SM, there is overall an increase of
23.2% (from 0.771 to 0.950) in the generalization scores
(33.3% for IMf and 14.8% for SM), when comparing DK-
FH to F*.
Complexity. Since the subprocesses are much smaller than
the flat model, the average complexity scores of subprocesses
of DK-FH are, as expected, significantly lower than F-FH or
F*. For DK-FH-IMf, the CFC is decreased by 90.6% (from
86.0 to 8.1), and 86.3% for DK-FH-SM (from 31.9 to 4.4),
when compared to the CFC scores of the models of F* on the
seven logs. The improvement is even more significant when it
is compared to the models by F-FH.
Fig. 6 shows the distribution of CFC of the submodels by
two approaches in more detail: DK-FH (blue boxplots) and
F-FH (purple lines). It shows the significant decrease in CFC
when using DK-FH.
Discussion. Overall, the results on the real-life logs have
shown that the quality of the submodels returned by the DK-
FH approach are higher than the one returned by either the
random clustering approachs or the flat discovery algorithms.
For example, compared to F*, DK-FH achieved an increase of
0.07 in fitness, 0.25 in precision, and 0.18 in generalization,
on average. As expected, the DK-FH outperforms the RC-FH.
Interestingly, the random activity clustering approach (RC-
FH) also shows relatively consistent improvements in the
qualities of obtained submodels, compared to the flat tree
approach and the flat discovery (F*), as listed in Tab. III and
shown in Fig. 5. This may suggest that discovering hierarchical
models may have a certain beneficial factor in terms of model
qualities, comparing to discovering a complex, flat model.
Additional experiments are needed to validate this observation.
However, if this is indeed the case, this may allow future
process discovery algorithms to focus on small processes (say
less than 10-20 activities), while designing other algorithms for
clustering the activities and discovering the process hierarchy.
A related, interesting observation is that for some subpro-
cesses and their sublogs, SM was able to discover better
models than IMf, and in other cases, IMf was able to find
better models than SM. Since FlexHMiner allows for the use
of any discovery algorithm, this suggests that one can build in
a selection strategy of the best subprocesses to further increase
the quality of the hierarchical models, as future work.
We also observed that it is rather trivial to flatten the
full model or certain subprocesses of interest, while allowing
abstracting the others, see Fig. 4. For example, in Fig. 2(c)
and (d), the logs L2and L3respectively show abstracting one
or two subprocesses. Applying a discovery algorithm on L2
returns a model where subprocess Cis abstracted; and for L3,
a model is returned where subprocesses Cand Lare abstracted,
while the detailed activities of subprocess Sare retained.
Fig. 3: The flat model discovered using F-FH-IMf on the BPIC15 1f log.
(a) The root process
(c)Subprocess “01_HOOFD_0”
(d) Subprocess “01_HOOFD_1” (e) Subprocess “01_HOOFD_2”
(b) Subprocess “01_HOOFD”
(a) The root process
Fig. 4: The root process and three subprocesses discovered by DK-FH-IMf on the BPIC15 1f log.
IMf
SM
Fig. 5: Significantly higher F1-scores achieved by DK-FH
(blue), followed by RC-FH (grey), compared to the F-FH
(purple) and the results reported in [8] (purple), on the seven
benchmark data sets (on the left IMf, and on the right SM).
V. RE LATE D WOR K
In this section, we discuss related works regarding hierar-
chical process discovery and event abstraction, specifically.
Following the unsupervised strategy, Bose and van der
Aalst [9] are one of the first who propose to detect reoccurring
consecutive activity sequences as subprocesses. This approach
treats concurrent subprocesses as running sequentially and
thus does not assume true concurrent/interleaving subspro-
cesses. Later, Tax et al. [17] propose an approach to generate
frequent subprocesses, also known as local process models.
This approach enables detecting interleaving subprocess in an
unsupervised manner, which is used to create abstracted logs.
Using the supervised strategy, the State Chart Miner
(SCM) [14] extends Inductive Miner (IM) and uses informa-
IMf
SM
BPIC12
BPIC15_1f
BPIC15_2f
BPIC15_3f
BPIC15_4f
BPIC15_5f
BPIC17f
BPIC12
BPIC15_1f
BPIC15_2f
BPIC15_3f
BPIC15_4f
BPIC15_5f
BPIC17f
0
50
100
150
CFC
CAlg
F-FH
F*
DK-FH
RC-FH
Fig. 6: A significant decrease in the complexity (CFC)
achieved by the DK-FH (blue), compared to the F-FH (F)
returned (purple lines) for the 16 data sets.
tion in the activity labels to create a hierarchy to discover
hierarchical models. SCM also focuses on sequential subpro-
cesses, where non-consecutive events of the same instance
are cut into separate traces. This assumption leads to the
discovery of models that are overly segmented and fail to
capture concurrent behavior, as shown in Fig. 1a. Furthermore,
SCM can only use IM for discovering subprocesses.
Mannhardt et al. [13] require users to define complete
behavioral models of subprocesses and their relations to com-
pute abstracted logs. This prerequisite of specifying the full
behavior of low-level processes put much burden on the users.
Moreover, it uses the alignment technique to compute high-
level logs which is computationally very expensive and can be
nondeterministic.
Other approaches assume additional attributes to indicate
the hierarchical information. Using a relational database as
input, Conforti et al. [12] assume that each event has a set of
primary and foreign keys that can be used as the subprocess
instance identifier, in order to determine subprocesses and
multi-instances. However, such event attributes may not be
common in most of the event logs. As an alternative, Wang
et al. [11] assume that the events contain start and complete
timestamps and have explicit information of the follow-up
events (i.e., the next intended activity, which they called
“transfer” attributes). Senderovich et al. [18] propose the use
of patient schedules in a hospital as an approximation to the
actual life-cycle of a visit. These approaches cannot be applied
in our case, since we do not find these attributes (such as
explicit causal-relations between events, the start and complete
timestamps, or the scheduling of activities) in our logs.
A very recent literature review conducted by van Zelst et al.
[19] provides an extensive overview and taxonomy for clas-
sifying different event abstraction approaches. In [19], Zelst
et al. studied 21 articles in depth and compared them among
seven different dimensions. One dimension is particularly im-
portant to distinguish our approaches, namely the supervision
strategy. None of the 21 methods enable both supervised and
unsupervised, whereas we have shown that we can used both
supervised (domain knowledge) and unsupervised (random
clustering) to discover an activity tree for event abstraction.
Our evaluation has shown FlexHMiner to be flexible and ap-
plicable in practice. It is worthy to mention that our approach
does assume that for each case, each subprocess is executed
at most once (i.e., single-instance), while a subprocess can
contain loops. As future work, we can extend the algorithm to
include, in addition to the abstraction and projection functions,
the multi-instance detection and segmentation techniques to
handle multi-instance subprocesses.
VI. CONCLUSION
In this work, we investigated the hierarchical process dis-
covery problem. We presented FlexHMiner, a general ap-
proach that supports flexible ways to compute process hierar-
chy using the notion of activity tree. We demonstrate this flexi-
bility by proposing three methods for computing the hierarchy,
which vary from fully supervised, using domain knowledge,
to fully automated, using a random approach. We investigated
the quality of hierarchical models discovered using these
different methods. The empirical evidence, using seven real-
life logs, demonstrates that the one using supervised approach
outperforms the one using random clustering in terms of the
four quality dimensions. But both methods outperform the flat
model approaches, which clearly demonstrates the strengths
of the FlexHMiner approach.
For future work, we plan to investigate different algorithms
for computing activity trees to further improve the quality of
hierarchical models. Also, the concept of activity trees can
be extended to data-aware or context-aware activity trees. For
example, an activity node can be associate with a data contraint
(context), so that the events labeled with the same activity but
have different data attributes (contexts) can be abstracted into
different subprocesses.
ACKNOWLEDGMENT
This research was supported by the NWO TACTICS project
(628.011.004) and Lunet Zorg in the Netherlands. We would
also like to thank the experts from the VUMC for their
extremely valuable assistance and feedback in the evaluation.
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