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structure. The proposed framework is applied on three real-world tag datasets and
the results are presented in Sect.
5.4
. Finally, Sect.
5.5
concludes the chapter.
5.2 Background
This section presents background material that is necessary for the subsequent
discussion. Some mathematical notation is provided in Sect.
5.2.1
and several
recent works that are pertinent to the chapter subject are discussed in Sect.
5.2.2
.
5.2.1 Notation
For folksonomies, we employ the definition presented in [
2
]. However, we do not
include the subtag/supertag relation nor the personomy construct that appear in the
original definition.
Definition 1.
A folksonomy is a tuple
, where U, R, T are finite sets
comprising respectively the users, resources and tags of the Collaborative Tagging
Systems under study, and Y is a ternary relation between them, i.e., Y
F
f
U
;
R
;
T
;
Y
g
U
R
T,
called tag assignments (TAS).
Since folksonomies are commonly represented in the form of networks, we will
adopt the common graph notation, according to which
G
(
V
,
E
) is a graph
consisting of the set
V
of nodes and the set
E
of edges. A natural way to model a
folksonomy is by use of a hypergraph, where
V
¼
¼
U
[
R
[
T
and
E
¼
{{
u
,
r
,
t
}|
(
u
,
r
,
t
)
Y
}. However, the hypergraph model is very rarely used in practice due to
its complexity, as well as due to the lack of efficient techniques for analyzing its
structure. Instead, the tripartite graph model, in which each hyper-edge {
u
,
r
,
t
}
∈
∈
Y
is reduced to three simple edges {(
u
,
r
)
T
}, is
used as an approximate representation for folksonomies. Further simplifications of
the model, for example, to bipartite graphs and to one-mode networks [
1
], are even
more frequently used for tackling specific analysis problems.
For instance, a very common folksonomy-derived graph is the tag co-occurrence
graph,
G
T
¼
∈
U
R
,(
u
,
t
)
∈
U
T
,(
r
,
t
)
∈
R
{
V
T
,
E
T
}, where nodes represent tags,
V
T
T
, and edges depict co-
occurrences between pairs of tags,
E
T
¼
T
}. Tag co-occurrence is
usually defined in the context of resources, i.e., when two tags are used together to
annotate the same resource, they are considered co-occurring. The number of times
that two tags co-occur in the context of some resource can be used as a weight of
their relation on the graph,
c
(
t
i
,
t
j
)
{(
t
i
,
t
j
)|
t
i
,
t
j
∈
.
4
There
¼
c
ij
¼j
{
∃
r
∈
R
|(
r
,
t
i
),(
r
,
t
j
)
∈
R
T
}
j
4
In the following, we refer to this kind of co-occurrence as
resource-based
tag co-occurrence.
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