=Paper= {{Paper |id=Vol-1698/CS&P2016_03_Tax&Alasgarov&Sidorova&Haakma_On-Generation-of-Time-based-Label-Refinements |storemode=property |title=On Generation of Time-based Label Refinements |pdfUrl=https://ceur-ws.org/Vol-1698/CS&P2016_03_Tax&Alasgarov&Sidorova&Haakma_On-Generation-of-Time-based-Label-Refinements.pdf |volume=Vol-1698 |authors=Niek Tax,Emin Alasgarov,Natalia Sidorova,Reinder Haakma |dblpUrl=https://dblp.org/rec/conf/csp/TaxASH16 }} ==On Generation of Time-based Label Refinements== https://ceur-ws.org/Vol-1698/CS&P2016_03_Tax&Alasgarov&Sidorova&Haakma_On-Generation-of-Time-based-Label-Refinements.pdf

On Generation of Time-based Label Refinements

Niek Tax1,2 , Emin Alasgarov1,2 , Natalia Sidorova1 , and Reinder Haakma2
1
Eindhoven University of Technology, Department of Mathematics and Computer
Science, P.O. Box 513, 5600MB Eindhoven, The Netherlands
{n.tax,n.sidorova}@tue.nl,{e.alasgarov}@student.tue.nl
2
Philips Research, Prof. Holstlaan 4, 5665 AA Eindhoven, The Netherlands
{niek.tax,reinder.haakma}@philips.com

Abstract. Process mining is a research field focused on the analysis of
event data with the aim of extracting insights in processes. Applying
process mining techniques on data from smart home environments has
the potential to provide valuable insights in (un)healthy habits and to
contribute to ambient assisted living solutions. Finding the right event
labels to enable application of process mining techniques is however far
from trivial, as simply using the triggering sensor as the label for sensor
events results in uninformative models that allow for too much behavior
(overgeneralizing). Refinements of sensor level event labels suggested
by domain experts have shown to enable discovery of more precise and
insightful process models. However, there exist no automated approach
to generate refinements of event labels in the context of process mining.
In this paper we propose a framework for automated generation of label
refinements based on the time attribute of events. We show on a case
study with real life smart home event data that behaviorally more specific,
and therefore more insightful, process models can be found by using
automatically generated refined labels in process discovery.

Keywords: Label Refinements, Process Discovery, Unsupervised Learning

1 Introduction

Process mining is a fast growing discipline that combines knowledge and tech-
niques from data mining, process modeling, and process model analysis [22].
Process mining techniques concern the analysis of events that are logged during
process execution, where event records contain information on what was done,
by whom, for whom, where, when, etc. Events are grouped into cases (process in-
stances), e.g. per patient for a hospital log, or per insurance claim for an insurance
company. Process discovery plays an important role in process mining, focusing on
extracting interpretable models of processes from event logs. One of the attributes
of the events is usually used as its label and its values become transition/activity
labels in the process models generated by process discovery algorithms.
The scope of process mining have broadened in recent years from business
process management to other application domains, one of them being analysis of
2

Table 1. An example of an event log from a smart home environment.

Id Timestamp Address Sensor Sensor value
1 03/11/2015 04:59:54 Mountain Rd. 7 Motion sensor - Bedroom 1
2 03/11/2015 06:04:36 Mountain Rd. 7 Motion sensor - Bedroom 1
3 03/11/2015 08:45:12 Mountain Rd. 7 Motion sensor - Living room 1
4 03/11/2015 09:10:10 Mountain Rd. 7 Motion sensor - Kitchen 1
5 03/11/2015 09:12:01 Mountain Rd. 7 Power sensor - Water cooker 1200
6 03/11/2015 09:15:45 Mountain Rd. 7 Power sensor - Water cooker 0
... 03/11/2015 . . . Mountain Rd. 7 ... ...
7 03/12/2015 01:01:23 Mountain Rd. 7 Motion sensor - Bedroom 1
8 03/12/2015 03:13:14 Mountain Rd. 7 Motion sensor - Bedroom 1
9 03/12/2015 07:24:57 Mountain Rd. 7 Motion sensor - Bedroom 1
10 03/12/2015 08:34:02 Mountain Rd. 7 Motion sensor - Bedroom 1
11 03/12/2015 09:12:00 Mountain Rd. 7 Motion sensor - Living room 1
... 03/12/2015 . . . Mountain Rd. 7 ... ...
12 03/14/2015 03:41:46 Mountain Rd. 7 Motion sensor - Bedroom 1
13 03/14/2015 05:00:17 Mountain Rd. 7 Motion sensor - Bedroom 1
14 03/14/2015 08:52:32 Mountain Rd. 7 Motion sensor - Bedroom 1
15 03/14/2015 09:30:54 Mountain Rd. 7 Motion sensor - Living room 1
16 03/14/2015 09:35:25 Mountain Rd. 7 Power sensor - TV 160
17 03/14/2015 10:27:37 Mountain Rd. 7 Power sensor - TV 0
... 03/14/2015 . . . Mountain Rd. 7 ... ...
... ... ... ... ...

events of human behavior with data originating from sensors in smart home envi-
ronments [19, 21, 20]. Table 1 shows an example of such an event log. Events in the
event log are generated by e.g. motion sensors placed in the home, power sensors
placed on appliances, open/close sensors placed on closets and cabinets, etc. Par-
ticularly challenging in applying process mining in this application domain is the
extraction of meaningful event labels that allow for discovery of insightful process
models. Simply using the sensor that generates an event (the sensor column in Ta-
ble 1) as event label is shown to produce non-informative process models that over-
generalize the event log and allow for too much behavior [21]. Abstracting sensor-
level events into events at the level of human activity (e.g. eating, sleeping, etc.)
using techniques closely related to techniques used in the activity recognition field
helps to discover more behaviorally more constrained and insightful process models
[20], but applicability of this approach relies on the availability of a reliable diary
of human behavior at the activity level, which is often just impossible to obtain.
In our earlier work [21] we showed that better process models can be discovered
by taking the name of the sensor that generated the event as a starting point for
the event label and then refining these labels using information on the time within
the day at which the event occurred. The refinements used in [21] were based on
domain knowledge, and not identified automatically from the data. In this paper,
we aim at automatic generation of semantically interpretable label refinements
that can be explained to the user, by basing label refinements on data attributes
of events. We explore methods to bring parts of the timestamp information to
the event label in an intelligent and fully automated way, with the end goal of dis-
covering behaviorally more precise and therefore more insightful process models.
We start by introducing basic concepts and notations used in this paper in
Section 2. In Section 3, we introduce a framework for the generation of event
labels refinements based on the time attribute. In Section 4, we apply this frame-
work on a real life smart home data set and show the effect of the refined event
labels on process discovery. We continue by describing related work in Section
5 and conclude in Section 6.
3

2 Preliminaries

In this section we introduce the notions related to event logs and relabeling
functions for traces and then define the notions of refinements and abstractions.
We also introduce the Petri net process model notation.
We use the usual sequence definition, and denote a sequence by listing its
elements, e.g. we write ha1 , a2 , . . . , an i for a (finite) sequence s : {1, . . . , n} → A
of elements from some alphabet A, where s(i) = ai for any i ∈ {1, . . . , n}; |s|
denotes the length of sequence s; s1 s2 denotes the concatenation of sequences s1
and s2 . A language L over an alphabet A is a set of sequences over A. Lp is the
prefix closure of a language L (with L ⊆ Lp ).
An event is the most elementary element of an event log. Let I be a set
of event identifiers, and A1 × · · · × An be an attribute domain consisting of n
attributes (e.g. timestamp, resource, activity name, cost, etc.). An event is a
tuple e = (i, a1 , . . . , an ), with i ∈ I and (a1 , . . . , an ) ∈ A1 × · · · × An . The event
label of an event is the attribute set (a1 . . . , an ); ei , and ea respectively denote
the identifier and label of event e. The timestamp attribute of an event is denoted
by at . E = I × A1 × · · · × An is a universe of events over A1 , . . . , An . The rows
of Table 1 are events from an event universe over the event attributes timestamp,
sensor, address, and sensor value.
Events are often considered in the context of other events. We call E ⊆ E
an event set if E does not contain any events with the same event identifier.
The events in Table 1 together form an event set. A trace σ is a finite sequence
formed by the events from an event set E ⊆ E that respects the time ordering
of events, i.e. for all k, m ∈ N, 1 ≤ k < m ≤ |E|, we have: σ(k)t ≤ σ(m)t . We
define the universe of traces over event universe E, denoted Σ(E), as the set of
all possible traces over E. We omit E in Σ(E) and use the shorter notation Σ
when the event universe is clear from the context.
Often it is useful to partition an event set into smaller sets in which events
belong together according to some criterion. We might for example be interested
in discovering the typical behavior within a household over the course of a day.
In order to do so, we can e.g. group together events with the same address and
the same day-part of the timestamp, as indicated by the horizontal lines in Table
1. For each of these event sets, we can construct a trace; time stamps define the
ordering of events within the trace. For events of a trace having the same time
stamps, an arbitrary ordering can be chosen within a trace.
An event partitioning function is a function ep : E → Tid that defines the
partitioning of an arbitrary set of events E ⊆ E from a given event universe E into
event sets E1 , . . . , Ej , . . . where each Ej is the maximal subset of E such that for
any e1 , e2 ∈ Ej , ep(e1 ) = ep(e2 ); the value of ep shared by all the elements of Ej
defines the value of the trace attribute Tid . Note that multidimensional trace at-
tributes are also possible, i.e. a combination of the name of the person performing
the event activity and the date of the event, so that every trace contains activities
of one person during one day. The event sets obtained by applying an event par-
titioning can be transformed into traces (respecting the time ordering of events).
4

An event log L is a finite set of traces L ⊆ Σ(E). AL ⊆ A1 × · · · × An denotes
the alphabet of event labels that occur in log L. The traces of a log are often
transformed before doing further analysis: very detailed but not necessarily infor-
mative event descriptions are transformed into some informative and repeatable
labels. For the labels of the log in Table 1, the sensor values could be abstracted
to on, and off or labels can be redefined to a subset of the event attributes, e.g.
leaving the sensor values out completely. Next to that, if the event partitioning
function maps each event from Table 1 to its address and the day-part of the
timestamp, these attributes (indicated in gray) become the trace attribute and
can safely be removed from individual events.
After this relabeling step, some traces of the log can become identically labeled
(the event id’s would still be different). The information about the number of
occurrences of a sequence of labels in an event log is highly relevant for process
mining, since it allows differentiating between the mainstream behavior of a
process (frequently occurring behavioral patterns) and exceptional behavior.
Let E, E 0 be an event universe. A function l : E → E 0 is an event relabeling
function. A relabeling function can be used to obtain more useful event labels than
the full set of event attribute values. We lift l to event logs. Let E, E1 , E2 be event
universes with E, E1 , E2 being pairwise different. Let l1 : E → E1 and l2 : E → E2
be event relabeling functions. Relabeling function l1 is a refinement of relabeling
function l2 , denoted by l1 l2 , iff ∀e1 ,e2 ∈E : l1 (e1 ) = l1 (e2 ) =⇒ l2 (e1 ) = l2 (e2 );
l2 is then called an abstraction of l1 .
The goal of process discovery is to discover a process model that represents the
behavior seen in an event log. A frequently used process modeling notation in the
process mining field is the Petri net [16]. Petri nets are directed bipartite graphs
consisting of transitions and places, connected by arcs. Transitions represent
activities, while places represent the enabling conditions of transitions. Labels
are assigned to transitions to indicate the type of activity that they model. A
special label τ is used to represent invisible transitions, which are only used for
routing purposes and not recorded in the execution log.
A labeled Petri net N = hP, T, F, AM , `i is a tuple where P is a finite set of
places, T is a finite set of transitions such that P ∩ T = ∅, F ⊆ (P × T ) ∪ (T × P )
is a set of directed arcs, called the flow relation, AM is an alphabet of labels
representing activities, with τ ∈ / AM being a label representing invisible events,
and ` : T → AM ∪ {τ } is a labeling function that assigns a label to each transition.
For a node n ∈ (P ∪ T ) we use •n and n• to denote the set of input and output
nodes of n, defined as •n = {n|(n0 , n) ∈ F } and n• = {n|(n, n0 ) ∈ F }. An example
of a Petri net can be seen in Figure 1, where circles represent places and squares
represent transitions. Gray transitions with smaller width represent τ transitions.
A state of a Petri net is defined by its marking M ∈ NP being a multiset
of places. A marking is graphically denoted by putting M (p) tokens on each
place p ∈ P . A pair (N, M ) is called a marked Petri net. State changes occur
through transition firings. A transition t is enabled (can fire) in a given marking
M if each input place p ∈ •t contains at least one token. Once a transition
fires, one token is removed from each input place of t and one token is added to
each output place of t, leading to a new marking. An accepting Petri net is a
5

p5 t6 p7
B E
t2
A D
p4 t5 p6
p1 p2 p3 p8
t1 t4 t7
C F
t3

Fig. 1. An example Petri net.

3-tuple (N, Mi , Mf ) with N a labeled Petri net, Mi an initial marking, and Mf
a set of final markings. Many process modeling notations, including accepting
Petri nets, have formal executional semantics and a model defines a language of
accepting traces L. For the Petri net in Figure 1, the language of accepting traces
is {hA, B, D, E, F i, hA, B, D, F, Ei, hA, C, D, E, F i, hA, C, D, F, Ei}.

3 A Framework for Time-based Label Refinements
To generate potential label refinements for every label based on time we take
a clustering based approach by identifying dense areas in time space for each
label. The time part of the timestamps consists of values between 00:00:00 and
23:59:59, equivalent to the timestamp attribute from Table 1 with the day-part of
the timestamp removed. This timestamp can be transformed into a real number
hourfloat representation in interval [0, 24). We chose to apply soft clustering (also
referred to as fuzzy clustering), which has the benefit of assigning to each data
point a likelihood of belonging to each cluster. A well-known approach to soft
clustering is based on the combination of the Expectation-Maximization (EM)
algorithm with mixture models, which are probability distributions consisting of
multiple components of the same probability distribution. Each component in the
mixture represents one cluster and the probability of a data point belonging to
that cluster is the probability that this cluster generated that data point. The EM
algorithm is used to obtain a maximum likelihood estimate of the mixture model
parameters, i.e. the parameters of the probability distributions in the mixture.
A well-known example of a mixture model is the Gaussian Mixture Model
(GMM), where the components in the mixture distributions are normal distri-
butions. The data space of time is, however, non-euclidean: it has a circular
nature, e.g. 23.99 is closer to 0 than to 23. This circular nature of the data space
introduces problems for GMMs, as shown in Figure 2. The GMM fitted to the
timestamps of the sensor events consists of two components, one with the mean at
9.05 and one with a mean at 20. The histogram representation of the same data
shows that some events happened just after midnight, which is actually closer on
the clock to 20 than to 9.05. The GMM however is unaware of the circularity of
the clock, which results in the mixture model that seems inappropriate when visu-
ally comparing with the histogram. The field of circular statistics (also referred to
as directional statistics), concerns analysis of such circular data spaces (cf. [14]).
Here, we introduce a framework for generating refinements of event labels
based on time attributes using techniques from the field of circular statistics.
This framework consists of three stages:
6

Fig. 2. The histogram representation and a Gaussian Mixture Model fitted to
timestamps values of the plates cupboard sensor in the van Kasteren data set [23].

Data-model pre-fitting stage A known problem with many clustering tech-
niques is that they return clusters even when the data should not be clustered.
In this stage we assess how many clusters the events of a sensor type contain.
Data-model fitting stage In this stage we cluster the events of a sensor type
by timestamp using a mixture consisting of components that take into account
the circularity of the data.
Data-model post-fitting stage In this stage the quality of the label refine-
ments is assessed from both a cluster quality perspective and a process model
(event ordering statistics) perspective.

3.1 Data-model pre-fitting stage

We now describe a test for uniformity, a test for unimodality, and a method to
select the number of clusters in the data.

Uniformity Check - Rao’s Spacing Test Rao’s spacing test [15] tests the
uniformity of the timestamps of the events from a sensor around the circular
clock. This test is based on the idea that uniform circular data is distributed
evenly around the circle, and n observations are separated from each other 360 n
degrees. The null hypothesis is that the data is uniform around the circle.
Given n successive observations f1 , . . . , fn , either clockwise orPcounterclock-
n
wise, the test statistics U for Rao’s Spacing Test is defined as U = 12 i=1 | Ti −λ |,
◦
◦
where λ = 360 n , Ti = fi+1 − fi for 1 ≤ i ≤ n − 1 and Tn = (360 − fn ) + f1 .

Unimodality Check - Hartigan’s Dip Test Hartigan’s dip tests [7] the null
hypothesis that the data follows a unimodal distribution on a circle. When the
null hypothesis can be rejected, we know that the distribution of the data is at
7

least bimodal. Hartigan’s dip test measures the maximum difference between the
the empirical distribution function and the unimodal distribution function that
minimizes that maximum difference.

Number of Component Selection - Bayesian Information Criterion The
Bayesian Information Criterion (BIC) [17] introduces a penalty for the number
of model parameters to the evaluation of a mixture model. Adding a component
to a mixture model increases the number of parameters of the mixture with the
number of parameters of the distribution of the added component. The likelihood
of the data given the model can only increase by adding extra components,
adding the BIC penalty results in a trade-off between number of components and
the likelihood of the data given the mixture model. BIC is formally defined as
BIC = −2 ∗ lnL̂ + k ∗ ln(n), where L̂ is a maximized value for the data likelihood,
n is the sample size, and k is the number of parameters to be estimated. A lower
BIC value indicates a better model. We start with 1 component, and iteratively
increase from k to k + 1 components as long as the decrease in BIC is larger than
10, which is the threshold for decisive evidence of high BIC [10].

3.2 Data-model fitting stage

We cluster events generated by one sensor using a mixture model consisting
of components of the von Mises distribution, which is a circular version of the
normal distribution. This technique is based on the approach of Banerjee et al.
[1], who introduce a clustering method based on a mixture of von Mises-Fisher
distribution components, which is a generalization of the 2-dimensional von Mises
distribution to n-dimensional spheres. A probability density function for a von
Mises distribution with mean direction µ and concentration parameter κ is defined
as pdf(θ | µ, κ) = 2πI10 (κ) eκ cos(θ−µ) , where mean µ and data point θ are expressed
in radians on the circle, such that 0 ≤ θ ≤ 2π, 0 ≤ µ ≤ 2π, κ ≥ 0. I0 represents
R 2π
1
the modified Bessel function of order 0, defined as I0 (k) = 2π 0 eκ cos(θ) dθ. As κ
approaches 0, the distribution becomes uniform around the circle. As κ increases,
the distribution becomes relatively concentrated around the mean µ and the von
Mises distribution starts to approximate a normal distribution. We fit a mixture
model of von Mises components using the package movMF [9] provided in R.

3.3 Data-model post-fitting stage

After fitting a mixture of von Mises distributions to the sensor events, we perform
a goodness-of-fit test to check whether the data could have been generated from
this distribution. We describe the Watson U 2 statistic [25], a goodness-of-fit
assessment based on hypothesis testing. The Watson U 2 statistic measures the
discrepancy between the cumulative distribution function F (θ) and the empirical
distribution function Fn (θ) of some sample θ drawn from some population and is
R 2π h R 2π i2
defined as U 2 = n 0 Fn (θ) − F (θ) − 0 Fn (φ) − F (φ) dF (φ) dF (θ).
8

Table 2. Estimated parameters for
a mixture of von Mises components
for bedroom door sensor events.

Cluster α µ (radii) κ
Cluster 1 0.76 2.05 3.85
Cluster 2 0.24 5.94 1.56

Fig. 3. BIC values for different numbers of
components in the mixture model.

Furthermore we assess the quality of refining the event label into a new
label for each cluster from a process perspective using the label refinement
evaluation method described in [21]. This method tests whether the log statistics
that are used in many process discovery algorithms become significantly more
deterministic by applying the label refinement.

4 Case Study
We show the results of our time-based label refinements approach on the real life
smart home data set described in van Kasteren et al. [23]. The van Kasteren data
set consists of 1285 events divided over fourteen different sensors. We segment
in days from midnight to midnight to define cases. Figure 4a shows the process
model discovered on this event log with the Inductive Miner infrequent [11] with
20% filtering, which discovers a process model that describes the most frequent
80% of behavior in the log. Note that this process model overgeneralises allowing
too much behaviour. At the beginning a (possibly repeated) choice is made
between five transitions. At the end of the process, the model allows any sequence
over the alphabet of five activities, where each activity occurs at least once.
We illustrate our proof of concept by applying the framework to the bedroom
door sensor. Rao’s spacing test results in a test statistic of 241.0 with 152.5 being
the critical value for significance level 0.01, indicating that we can reject the null
hypothesis of a uniformly distributed set of bedroom door timestamps. Hartigan’s
dip test results in a p-value of 3.95 × 10−4 , indicating that we can reject the null
hypothesis that there is only one cluster in the bedroom door data. Figure 3 shows
the BIC values for different numbers of components in the model. The figure
indicates that there are two clusters in the data, as this corresponds to the lowest
BIC value. Table 2 shows the mean and κ parameters of the two clusters found by
optimizing the von Mises mixture model with the EM algorithm. A value of 0 = 2π
radii equals midnight. After applying the von Mises mixture model to the bedroom
door events and assigning each event to the maximum likelihood cluster we obtain
a time range of [3.08-10.44] for cluster 1 and a time range of [17.06-0.88] for cluster
9

(a)

(b)

Fig. 4. Process models discovered on the van Kasteren data with sensor-level labels (a)
and refined labels (b) with the Inductive Miner infrequent (20% filtering) [11].

2. The Watson U 2 test results in a test statistic of 0.368 and 0.392 for cluster 1 and
2 respectively with a critical value of 0.141 for a 0.01 significance level, indicating
that the data is likely to be generated by the two von Mises distributions found.
The label refinement evaluation method [21] finds statistically significant differ-
ences between the events from the two bedroom door clusters with regard to their
control-flow relations with other activities in the log for 10 other activities using
the significance level of 0.01, indicating that the two clusters are different from a
control-flow perspective. Figure 4b shows the process model discovered with the
Inductive Miner infrequent with 20% filtering after applying this label refinement
to the van Kasteren event log. The process model still overgeneralizes in general,
but the label refinement does help restricting the behavior, as it shows that the
evening bedroom door events are succeeded by one or more events of type groceries
cupboard, freezer, cups cupboard, fridge, plates cupboard, or pans cupboard, while
the morning bedroom door events are followed by one or more frontdoor events.
It seems that this person generally goes to the bedroom in-between coming home
from work and starting to cook. The loop of the frontdoor events could be caused
by the person leaving the house in the morning for work, resulting in no logged
events until the person comes home again by opening the frontdoor. Note that in
Figure 4a bedroom door and frontdoor events can occur an arbitrary number of
10

Fig. 5. Inductive Miner infrequent (20% filtering) [11] result after a second label
refinement.

times in any order. Figure 4a furthermore does not allow for the bedroom door to
occur before the whole block of kitchen-located events at the beginning of the net.
Label refinements can be applied iteratively. Figure 5 shows the effect of a
second label refinement step, where Plates cupboard using the same methodology
is refined into two labels, representing time ranges [7.98-14.02] and [16.05-0.92]
respectively. This refinement shows the additional insight that the evening version
of the Plates cupboard occurs in directly before or after the microwave.

5 Related Work
Refining event labels in the event log is closely related to the task of mining
process models with duplicate activities, in which the resulting process model can
contain multiple transitions/nodes with the same label. From the point of view of
the behavior allowed by a process model, it makes no difference whether a process
model is discovered on an event log with refined labels, or whether a process
model is discovered with duplicate activities such that each transition/node of
the duplicate activity precisely covers one versions of the refined label. The first
process discovery algorithm capable of discovering duplicate tasks was proposed by
Herbst and Karagiannis in 2004 [8], after which many others have been proposed,
including the Genetic Miner [4], the Evolutionary Tree Miner [2], the α∗ -algorithm
[12], the α# -algorithm [6], the EnhancedWFMiner [5], and a simulated annealing
based algorithm [18]. An alternative approach has been proposed by Vázques-
Barreiros [24] et al., who describe a local search based approach to repair a
process model to include duplicate activities, starting from an event log and a
process model without duplicate activities. Existing work on mining models with
duplicate activities all base their duplicate activities on how well the event log
fits the process model, and do not try to find any semantic difference between
the multiple versions of the activities in the form of data attribute differences.
The work that is closest to our work is the work by Lu et al. [13], who describe
an approach to pre-process an event log by refining event labels with the goal of
discovering a process model with duplicate activities. The method proposed by
Lu et al., however, does not base the relabelings on data attributes of those events
but instead bases them solely on the control flow context, leaving uncertainty
whether two events relabeled differently are actually semantically different.
11

Another area of related work is data-aware process mining, where the aim is to
discover rules with regard to data attributes of events that decide decision points
in the process. De Leoni and van der Aalst [3] proposed a method that discovers
data guards for decision points in the process based on alignments and decision
tree learning. This approach relies on the discovery of a behaviorally well-fitting
process model from the original event log. When only overgeneralizing process
models (i.e. allowing for too much behavior) can be discovered from an event log,
the correct decision points might not be present in the discovered process model
at all, resulting in this approach not being able to discover the data dependencies
that are in the event log. Our label refinements use data attributes prior to process
discovery to enable discover more behaviorally constrained process models by
bringing parts of the event attribute space to the event label.

6 Conclusion & Future Work

We have proposed a framework based on techniques from the field of circular
statistics to refine event labels automatically based on their timestamp attribute.
We have shown through a proof of concept on a real life event log that this
framework can be used to discover label refinements that allow for discovery of
more insightful and behaviorally more specific process models. An interesting
area of future work is to explore the use of other types of event data attributes to
refine labels, e.g. power values of sensors. A next research step would be to explore
label refinements based on multiple data attributes combined. This would bring
challenge of clustering on partially circular and partially euclidean data spaces.

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