what-when-how
In Depth Tutorials and Information
(
Z
v
)
dg
results from
Z
v
by setting off-diagonal entries to zero, and
P
v
∞
is the limiting
matrix of
P
v
with each row of
P
v
∞
as
π
T
, or
P
v
∞
=
e
π
T
, where
e
is a column vector
with all ones. he matrix of the irst-passage time of the original CTMC
M
is
1
(
M
=
v
M
)
+
Λ
(
M
)
v of
v dg
(3.38)
where
Λ =
( )
1
(
M
v
)
dg
results from
M
v
by setting off-diagonal entries to zero,
and (
M
v
)
of
results from
M
v
by setting diagonal entries to zero. hus, the rank score
for each user
j
is estimated as
diag q
i
−
1
R j
( )
=
(3.39)
1
∑
m
ij
−
|
N
1
|
i
≠
j
As introduced in Section 2.2.4, the cascade model describes the probability of user
behavior, whether a user adopts an innovation from his neighbors or not. his
model can be also employed in predicting the diffusion of innovation. If we predict
each user behavior at each time point, then we can predict the whole process of
innovation propagation. Kimura and Saito [69] considered the problem of finding
influential nodes for innovation propagation in a large-scale social network and
proposed two natural special cases of the Independent Cascade Model (ICM) such
that a good estimate of the expected number of nodes influenced by a given set of
nodes can be efficiently computed. Saito et al. [70] focused on the independent
cascade model and defined the likelihood for information diffusion episodes where
an episode means a sequence of newly active nodes. hen Neal and Hinton [51] pre-
sented a method for predicting diffusion probabilities by using the EM algorithm.
Besides considering the linking relationship and previous behavior of the users,
investigators also studied other influence factors of information propagation.
Choudhury et al. [66, 67] developed a computational framework for predicting
communication low in social networks based on several contextual features. he
authors determined the intent to communicate and communication delay between
users based on three contextual features in a social network, corresponding to the
neighborhood context, topic context, and recipient context. he intent to com-
municate and communication delay are modeled as regression problems, which are
efficiently estimated using Support Vector Regression.
References
1. J. Scott. 2000.
SocialNetworkAnalysis:AHandbook.
Sage Publications, London, 2nd ed.
2. N.T.J. Bailey.
heMathematicalheoryofInfectiousDiseasesandItsApplications
, Hafner
Press, New York, 1975.
