what-when-how
In Depth Tutorials and Information
the tendency probability of a user's behavior based on the user's individual interest
in a topic.
∏
2
s
2
f x
(
)
=
k
−
(
x
−
x
)
∗
e
−
ki
,
k
>
1
(5.1)
n
n i
−
i
i
=
1
he function
f
(
-
) also interprets the input variables
x
n
, which is the behavior
state of user
a
about discussing the topic at time
n
. When the variable
x
n
is 1,
the function value is directly proportional to user
a
's probability of attending a
discussion on the topic at time
n
. When the variable
x
n
is 0, the function value is
not directly proportional to the probability of user
a
attending a discussion on the
topic at time
n
. he variable
k
i
is a parameter that must be estimated, while
s
is the
available duration of the individual interest factor. his individual interest factor is
when the user's behavior at time
n
only associates with the behavior from time
n
−
s
to time
n
− 1. his value can be evaluated by experience.
he more frequent
x
n−i
equals
x
n
, the larger the output of the function will
be and, therefore, the larger the probability. his can be stated as, the more fre-
quently that the predicted behavior of a user
a
at time
n
is the same as the previous
behavior at time
n − i
, the more probable that the predicted behavior will happen.
Conversely, the less frequently the behavior of user
a
at time
n
is the same as the
previous behavior, then it will be less probable that the predicted behavior will hap-
pen in the future.
Next, considering the second hypothesis, another formula can be derived. his
formula is determined on the premise that, as more users attend a group discussion,
the attending users will attract other users to join, causing more users to attend
and, therefore, increasing any user's probability. he original users that inluence
other users will also be more likely to attend after attracting a larger group. Based
on this concept, the behavior tendency function
h
(
-
)is given for a user
a
at time
n
.
he function calculates the probability of the behavior trend by the group behavior.
his behavior tendency function is as follows:
∏
1
s
ʹ
=
2
x
n
∗
−
l
>
h x
(
)
l
+
r
−
e
,
l
1
(5.2)
1
j
j
j
i
=
1
his function requires the derivation of
r
from another formula, the changing ratio
of the number of users, which is as follows:
||
G n
(
−
j
) ||
+
||
G n
(
− −
j
1
) ||
+
||
G n
(
− −
j
2
) ||
+
1
=
1
(5.3)
r
− −
+
− −
+
− −
+
||
G
(
n
j
1
) ||
||
G n
(
j
2
) ||
||
G n
(
j
3
) ||
In the changing ratio of the number of users function ||
G
(
n
−
j
)|| represents the total
number of users who attend the discussion at time
n
-
j
. he output,
r
, is derived
