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Hypothesis.2: Group behavior factor. Assuming that the larger the number of
users who attend the discussion on the topic at present and have attended in
the past, T increases, the more probable that they will attend the discussion
the next time.
Hypothesis.3: Time lapse factor. Assuming that the longer the interval between
the present and peak time, the less probable that users will attend the discus-
sion the next time.
Based on Hypothesis 1, the behavior tendency function f ( x ) is given for user a at
time n (1 <n<N ), from which the tendency probability of the user's posting behav-
ior can be calculated as follows:
s
2
1
2
[
(
x
x
) ]
=
>
f x
(
)
k
e
k
,
k
1
(3.4)
n
n i
i
i
i
i
=
where x n is the behavior state of user a regarding posting on a topic at time n . When
x n is 1, the value of the function is in direct proportion to the probability of user a
attending the discussion at time n , and contrarily when x n is 0. K i is a parameter to
be estimated, e is the base of the Napierian logarithm, and s is the available duration
of the individual interest factor, which means user behavior at time n only associ-
ates with the behavior from time n−s to time n − 1 and can be evaluated by experi-
ence. he more frequently x n-i equals x n , the larger the value of the function. hat
is, the more frequently the predicted behavior of user a at time n is the same as the
previous behavior, the larger the probability of the predicted behavior happening,
and contrarily, the lesser the probability.
Based on Hypothesis 2, the behavior tendency function h ( x ) is given for user a
at time n (1 <n<N ), from which the probability of the group behavior trend of
can be calculated.
s
'
1
1
=
(
2
x n
1
)
l
>
h x
(
)
l
+
r
e
,
l
1
(3.5)
j
j
j
j
=
||
G n
(
j
) ||
+
||
G n
(
− −
j
1
) ||
+
||
G n
(
− −
j
2
) ||
+
1
=
1
(3.6)
r
− −
+
− −
+
− −
+
||
G
(
n
j
1
) ||
||
G n
(
j
2
) ||
||
G n
(
j
3
) ||
where G ( n-j ) is the total number of users who attend the discussion at time
n− j , and r is the changing ratio of the number of users that is calculated by divid-
ing the total number of users who are involved from time n−j to n−j−2 with the
total number of users from time n−j−1 to n−j−3 . If the total number decreases
in the duration, r is less than 1. s' is the available duration of group behavior factor,
which means the user behavior at time n only associates with the group behavior
from time n−s' to time n − 1, and can be evaluated by experience. L j is a parameter
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