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activity distance in a heterogeneous space with
dist
h
(
a
1
,a
2
) and in a homoge-
neous vector space with
dist
t
(
a
1
,a
2
), where
t
is the respective activity property
type. Both distance measures can be employed for activity aggregation. If the
user wants to make use of one activity property type
t
only, the distance is de-
fined by
dist
t
. To cluster activities according to several activity property types,
dist
h
can be employed. In addition, we introduce an alternative distance measure
dist
agg
that aggregates multiple homogeneous distance measures
dist
t
:
1
dist
agg
(
a
1
,a
2
)=
w
t
·
dist
t
(
a
1
,a
2
)
(3)
|
T
|
∀t∈T
In Equation 3, the set
T
corresponds to the activity property types that appear
in process model collection
c
. Then, function
dist
agg
is the weighted average
value of distance measures in the vector spaces corresponding to the available
activity property types. Coecient
w
t
is the weight of
dist
t
indicating the impact
of the activity distance according to property type
t
. We reference all the weights
in Equation 3 as
W
=(
w
t
1
,...,w
t
n
), where
n
=
|
T
|
. In the remainder of this
section we will explain the role of vector
W
.
2.4 Process Model Collection Abstraction Fingerprint
The application of different abstraction operations to one process model leads to
various abstract representations of the modeled business process. The differences
between abstraction operations are explained by their pragmatics, i.e., various
abstraction purposes. If the abstraction is realized by a human, the modeling
habits of the designer are reflected in the abstraction operation as well. Hence,
abstraction pragmatics and modeling habits of the designer are inherent proper-
ties of the abstraction operation and together form an
abstraction style
.Weuse
vector
in Equation 3 to model an abstraction style.
From the user perspective vector
W
W
is the tool to express the desired abstrac-
tion style. We foresee two scenarios how vector
W
can be obtained. In the first
W
scenario, the user explicitly specifies
. This approach is useful if the user wants
to introduce a new abstraction style. However, coming up with an appropriate
value for
W
may be challenging. Hence, the second scenario implies that vector
is mined from a process model collection enriched with subprocess relation
(formalized with
σ
in Definition 3). The discovered vector is a “fingerprint” of
the process model collection with respect to the used abstraction style. We will
now describe an approach how vector
W
W
can be discovered from such a process
model collection.
The discovery process of a model collection's abstraction fingerprint is driven
by the following argumentation. Activities of a process model collection are ag-
gregated into aggregated activities, i.e. subprocess placeholders, by the model
designer. We aim to achieve an activity clustering algorithm that approximates
this aggregation behavior of a human. This is possible if an activity distance mea-
sure employed by the algorithm resembles the criteria that a human designer uses
to aggregate activities into a subprocess. The exact criteria are unknown. Yet,
