Information Technology Reference
In-Depth Information
Where:
-
Parameters
ρ
a
,ρ
t
satisfy
0
≤
ρ
a
,ρ
t
,ρ
a
+
ρ
t
≤
1
.
-
F
(
a
before
→
act
t
)
is frequency of
a
before
→
act
t
(transition from
a
before
to
act
t
).
-
F
(
act
t
→
a
after
)
is frequency of
act
t
→
a
after
(transition from
act
t
to
a
after
).
-
F
(
act
t
,t
)
is frequency of
act
t
at time
t
.
-
F
(
act
t
,l
)
is frequency of
act
t
in location
l
.
u
a
after
action
before
action
?
time_1
u
j
before
action
after
action
act
1
act
2
time_b
time_t
t
jb
t
ab
t
j1
t
j2
t
jf
t
af
t
Fig. 7.
An example of plural missing actions
4.3 Prediction Based on Execution Time of Action
Figure 7 explains an example of plural missing actions. In this example, we need to
determine that
u
a
did
act
1
or
act
2
at time
t
. We can solve this problem based on the
execution time of these actions done by user
u
j
.
Let
time b
,
time
1
are execution time of before action,
act
1
done by the similar user
u
j
respectively. We suppose that it took the same execution time for
u
a
and
u
j
did the
same action. Based on this supposition, we can use Equation 3 to determine that
u
a
did
act
1
or not.
⎧
⎨
time t
time b
(
diff
<
0)
T
(
u
j
,act
1
)=
1
(0
≤
diff
≤
time 1
)
(3)
⎩
time
1
diff
(
time 1
<
diff
)
where,diff
=
time t
−
time b.
4.4 Prediction Formula
Combination of Equation 1, Equation 2, and Equation 3, we can calculate
P
u
a
→act
t
as
Equation 4.
⎛
⎞
ω
(
u
j
,act
t
)
∗
S
(
u
j
,u
a
)
∗
T
(
u
j
,act
t
)
⎝
⎠
j
=1
,L
P
u
a
→act
t
=
α
)
L
(4)
+(1
−
α
)
P
(
act
t
)
