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| {
Q c
(
) |
S Q c
⊆
(
)& (
Q c
)
∈
D
} |
=
i
i
i
Supp S
( )
(3.18)
D
|
D
|
where |
D
| is the total number of topic blog sequences in the database. he support
measure takes on values from 0 through 1. he more the topic blog sequences sup-
porting a blog sequence, the higher the support value of the blog sequence.
Deinition5.
[Strength] Given a blog sequence database
D
, a latency threshold
δ
, and a blog sequence
S
=
{
, the strength of the sequence, denoted as
b b
,
,...,
b
m
}
1
2
StregD
,
δ
(S), is
{
Q Lat M Q S
|
(
(
,
))
≤
δ
,
S Q Q D
⊆
,
∈
}
=
Streg
D
,
( )
S
(3.19)
δ
⊆
,
∈
{
Q S Q
|
Q D
}
hat is, the strength of a blog sequence is the fraction of supporting topic blog
sequences that have the latency of their matched topic blog subsequences less than
or equal to the given latency threshold.
Given a blog sequence database, we are interested in blog sequences that are
not only supported frequently by the database but also by topic blog sequences
that propagate information quickly. hus, we deine an Information Difusion Path
(IDP) as a blog sequence satisfying constraints specified as follows.
Deinition6
. [IDP] Given a blog sequence database
D
, a support threshold
α
,
a latency threshold
δ
, and a strength threshold
β
, a blog sequence
S
is an IDP if (1)
Supp S
D
( )
≥ β
.
For instance, given the support threshold
α
= 0.4, the latency threshold
δ
= 3
and the strength threshold
β
= 0.6, the blog sequence
S
D
( )
≥ α
, and (2)
Streg
S
= <
>
b b
is an IDP since
1 2
0 67
β
.
hen, the problem of information diffusion path mining can be formally stated
as follows. Given a blog sequence database
D
, a support threshold
α
, a latency
threshold
δ
, and a strength threshold
β
, the problem of information diffusion path
mining is to discover the set
{
Supp S
D
( )
=
0 6
α
and
Streg
.
≥
D
( )
S
=
.
≥
α
δ
.
Furthermore, Kossinets et al. [57] analyzed the temporal dynamics of the infor-
mation low pathway using online data, including e-mail communication among
the faculty and staf of a large university over a 2-year period. he authors pro-
posed a framework for analyzing this kind of systemic communication as shown
in Figure 3.2. In the figure, a complete communication history for a group of five
people over three days is shown. (Edges are annotated with the one or more times
at which directed communication took place.) Based on a long period data, the
latency, speed, and frequency of communication can be analyzed using this frame-
work. Although this framework is constructed for e-mail communication, it can be
also used to analyze the information propagation pathway for IM social network
and blogosphere. While analyzing the information low pathway in blogosphere is
S Supp S
|
( )
≥
&
Streg
( )
S
≥
}
D
D
,
