what-when-how
In Depth Tutorials and Information
Combining the variables of the original three formulas and simplifying, the follow-
ing final formula is given:
{
}
{
}
ʹ
s
s
2
x n
(
1
+
r
)
l
k
2
(
x
x
)
2
B
k
l
1
B
j
n
n i
i
j
i
=
1
j
=
1
>
>
λ
>
P x
(
)
,
k
1
l
1
,
0
(5.6)
n
i
j
(
B t
)
λ
x
n
p
he final step is to estimate the parameters k i and l j . Using the maximum likelihood
estimation (MLE) method, the following formulas could be determined:
2
[
]
(
x
x
)
2
n
n i
=
A
(5.7)
k
i
q
1
[
]
+
r
(
2
x
)
n
1
=
A
l
(5.8)
j
q
he variables are the same as in the previous equations, except for the addition
of new variables q and A . he variable q represents a total number of users in the
model, and the variable A represents the universal set of behaviors and users. If x n is
set as 1, then the value of χ ( x will have a positive correlation with P ( x n ).
he results from testing this probability model are shown as follows:
It can be observed from Figures 5.3-5.5 that the predicted and actual results
are very similar and, in fact, are relatively correlated. Figure 5.4 represents the best
140
Predicted data
Real data
120
100
80
60
40
20
0
0
5
10
15
20
Time (Day)
25
30
35
40
45
Figure 5.3
Predicted and actual results from topic 1. (From Y. Zhou et al.,
Predictingthetendencyoftopicdiscussionontheonlinesocialnetworksusinga
dynamicprobabilitymodel,in Conference on Hypertext and Hypermedia ,2008,
pp.7-11.)
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