what-when-how
In Depth Tutorials and Information
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