what-when-how
In Depth Tutorials and Information
to be estimated.
e
is the base of the Napierian logarithms.
x
n
is the predicting behav-
ior state of user
a
at time
n
; if
x
n
is equal to 1, then (2
x
n
−
1) is 1, so the more the
frequencies in which
r
is larger than 1, the larger the value of the behavior tendency
function, which shows that the more the total number of users who discuss the
topic, the larger the probability of one user attending the discussion, and contrarily,
the lesser the probability.
Based on Hypothesis 3, the behavior tendency function
g
(
x
) is given for user
a
at time
n
(1
<n<N
), from which the probability of behavior trend by the time
lapse factor can be calculated.
1
g x
( )
=
,
λ
>
0
(3.7)
−
(
n t
p
)
λ
⋅
x
n
where
n
is the time point to be predicted,
t
p
is the peak time when the number of
participators is the largest from initial time to time
n
,
λ
is the lapse exponential
coefficient (usually is 0.5−1) to be evaluated by experience, and
x
n
is the predicting
behavior state of user
a
at time
n
. In formula 3.9, if
x
n
is equal to 1, then the value
of the function is larger than 1, and the larger
n
is, the less the value of the behavior
tendency function will be. his demonstrates that the longer the interval from peak
time to predicting time, the less the probability of user behavior in attending the
discussion; if
x
n
is equal to 0, the value of the behavior tendency function is 1.
Considering all the three hypothesis factors, the behavior tendency function
χ
(
x
) is given for user
a
at predicting time
n
.
s
s
'
∏
∏
[
2
−
(
x
−
−
x
) ]
2
(
2
x
n
−
1
)
⋅
⋅
1
+ +
(
r
1
)
⋅
−
l
{
k
e
−
k
} {
l
e
}
n
n
i
j
i
i
j
χ
i
=
1
j
=
1
P x
(
) ~ (
x
)
=
f x
(
)
⋅
h x
(
)
⋅
g x
(
)
=
n
−
(
n t
p
)
λ
⋅
x
n
and
k
>
1
,
l
>
1
,
λ
>
0
(3.8)
i
j
where
P
(
x
n
) is the probability of the tendency to attend the discussion or not.
P
(
x
n
)
has positive correlation with
χ
(
x
).
All of the
q
user behavior in the universal set
A
can be expressed as
a
:
x
,
a
:
x
,...,
a
:
x
(3.9)
1
a
1
2
a
2
q
aq
hey have estimated the parameters in formula 8 by the Maximum Likelihood
Estimate (MLE) method. he results are as follows:
=
χ
⋅
χ
⋅ ⋅ ⋅
χ
ln ( )
L q
ln[ (
x
)
(
x
)
(
x
)]
a
1
a
2
aq
s
s
'
(3.10)
∑
∑
∑
=
{
{[
2
−
(
x
−
x
) ] ln
⋅
k
−
k
}
+
{{
1
+
r
−
} ln
⋅
l
−
l
}}
2
(
2
x
n
1
)
n
n i
−
i
i
j
j
A
i
=
1
j
=
1
