Information Technology Reference
In-Depth Information
QA
data
Raw
data
FA
data
Fig. 2.
Example of a vector space formed by dimensions
FA data, QA data, Raw data
is associated with a property value
p
j
∈
P
i
, the corresponding vector dimension
π
j
(
v
a
) has value 1; otherwise, the dimension
π
j
(
v
a
)hasvalue0:
v
a
)=
1
,
props
i
(
a
);
0
,
otherwise.
For process model
m
in Fig. 1, activities
Prepare data for quick analysis
and
Prepare data for full analysis
correspond, respectively, to vectors
if
p
j
∈
π
j
(
v
1
=(0
,
1
,
1)
and
v
2
=(1
,
0
,
1) in the vector space with dimensions
FA data, QA data, Raw
data
, see Fig. 2.
Similarity of two vectors in the space is defined by the angle between these
vectors: the larger the angle, the more distant the activities are. Typically, the
cosine of the angle between two vectors is used as a vector similarity measure:
v
a
2
v
a
1
v
a
2
v
a
1
·
sim
(
a
1
,a
2
)=
cos
(
v
a
1
,v
a
2
)=
(1)
Then, the distance between two activities is:
dist
(
a
1
,a
2
)=1
−
sim
(
a
1
,a
2
)
(2)
By construction the vector dimension values are non-negative. Hence, the activity
similarity and activity distance measures vary within the interval [0
,
1].
For a process model collection
c
=(
M, A, P, σ
) we distinguish two types of
vector spaces. On the one hand, a vector space can be formed by the dimen-
sions corresponding to the activity property values disregard their type, i.e., all
elements of
P
. We reference such spaces as
heterogeneous vector spaces
.Anexam-
ple of a heterogeneous vector space is a space with 6 dimensions
Analyst, Clerk,
FA data, QA data, Raw data
,and
Senior analyst
. On the other hand, a vector
space can be formed by the dimensions corresponding to the activity property
values of a particular type. Given an activity property type
t
,suchaspaceis
formally defined by the set
P
t
=
. We refer to such spaces
as
homogeneous vector spaces
. Fig. 2 provides an example of a homogeneous
vector space formed by activity properties of type
Data object
.Wedenotethe
{∀
p
∈
P
:
type
(
p
)=
t
}
