what-when-how
In Depth Tutorials and Information
by dividing the total number of users who are involved from time
n
-
j
to
n
-
j
-
2
with the total number of users involved from time
n
-
j-1
to
n
-
j-3
. If this total
number decreases as time goes on,
r
will turn out to be less than 1.
In the original function, the behavior tendency function
s
' is the available dura-
tion of the group behavior factor, meaning that user
a
's behavior at time
n
only
associates with the group behavior during the timeframe (
n−s'
,
n−1
). he variable
l
j
is a parameter that must be estimated, much like the variable
k
i
from the behavior
tendency function from the irst hypothesis. he variable
x
n
is the predicting behav-
ior state of user
a
at time
n
. If this variable is equal to 1, then
r
will be larger than
1 more frequently than if
x
n
does not equal 1. his shows that, as the total number
of users who attend the topic discussion increases, the higher the probability that
one of the user's behavior in the future will be to attend the same discussion on the
same topic.
Finally, based on the third and final hypothesis, a final formula can be derived.
his final formula is based on the premise that a given user will no longer be inter-
ested in a specific topic after a long-enough period of time has passed since the last
topic discussion was attended by the user. Also, the total number of participators
will decrease after the peak time, the time when the largest numbers of users attend.
his decline rate will increase with the augmentation of the interval form from the
peak time. Based on these statements, the following formula is given:
1
g x
(
)
=
,
λ
>
0
(5.4)
−
(
n t
p
)
λ
∗
x
n
his final behavior tendency function,
g
(
-
), is given for a specific user
a
at a given
time
n
. his formula calculates the probability of behavior trend by the time lapse
factor. he value
n
is actually the time point that will be predicted, and
t
p
is the
peak time or the time between the time interval (0,
n
) when the number of par-
ticipators was the largest. he value
λ
is the lapse exponential coefficient, which is
typically between 0.5 and 1, and this value must be evaluated by experience. he
value
xn
represents the predicting behavior state of user
a
at time
n
.
In this particular behavior tendency function,
g
(
-
), if
x
n
is equal to 1, then
g
(
-
)
will be greater than 1, whereas the larger
n
becomes, the smaller
g
(
-
) will be. his
shows that the longer the interval from the peak time to the predicted time, the
lower the probability of the user attending the discussion on the same topic again
in the future. Also, when
x
n
is equal to 0, the output will be 1.
Given these three hypotheses, the final behavior tendency function
χ
(
-
) is given
as follows for user
a
at time
n
:
∼
χ
(5.5)
P x
(
)
(
x
)
=
f x
(
)
∗
h x
(
)
∗
g x
(
)
n
he value
P
(
x
n
) represents the probability of the tendency of attending the dis-
cussion. his probability positively correlates with
χ
(
x
as shown in the formula.
