what-when-how
In Depth Tutorials and Information
∑
[
2
−
(
x
−
−
x
) ]
2
n
n i
d
ln ( )
L q
dk
2
−
(
x
−
x
)
∑
2
(3.11)
=
n
n i
−
− = ⇒ =
A
{
1
}
0
k
i
k
q
i
i
A
∑
+
{
1
r
(
2
x
n
−
1)
}
+
d
ln ( )
L q
dl
∑
1
r
l
(
2
x
−
1
)
n
(3.12)
=
{
− = ⇒ =
1
}
0
l
A
j
q
j
j
A
According to formulas 11 and 12, the parameters in formula 8 can be estimated by
sample data, and the value of the behavior tendency function
χ
(
X
) can be calcu-
lated by setting
x
n
as 1 and 0. If
x
n
is 1,
χ
(
X
) has positive correlation with
P
(
x
n
=
1);
if
x
n
is 0,
χ
(
X
) has positive correlation with
P
(
x
n
=
0). After normalizing
χ
(
X
), the
values of
P
(
x
n
=
1) and
P
(
x
n
=
0) are obtained.
Figure 3.1 shows the comparison between real data and the predicting results
about two topics; and
x
axis is time whose unit is day,
y
axis is the number of par-
ticipators whose unit is user; blue line with diamond figure corresponds to the real
data, while black line with cross igure corresponds to the predicting result. he
values of
s
,
s
' and
λ
are 7, 3 and 0.5 respectively; and the other parameters are cal-
culated by MLE which has been mentioned in formula 11 and 12.
180
Predicting data
Real data
160
140
120
100
80
60
40
20
0
0
5
10
15
20
Time (day)
25
30
35
40
Figure3.1
Comparisonbetweenrealdataandthepredictedresults.
