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where
is defined as the
feature values in the left-hand side of the frequent action term
t
j
, and
Right
(
s
i
,
k
,
s
i
,
l
)
=
(
[
(
x
i
,
F
(
x
i
)
k
)
]
,
[
(
x
i
,
F
(
x
i
)
l
)
]
)
,
x
i
∈
X
,
Left
(
t
j
)
(
t
j
)
is the
right-hand side of
t
j
such that if
t
j
=[
(
a
l
1
ₒ
a
r
1
)
∧
(
a
l
2
ₒ
a
r
2
)
∧···∧
(
a
ln
ₒ
a
rn
)
]
then
Left
.
The likelihood support of action term measures the transition likelihood of their
attribute values but it neither takes into consideration the conflicts of action terms
nor handles the meta-actions comparison in a normalized way. A more sophisticated
way to evaluate action terms is by computing their likelihood confidence, and thus
a possible meta-action confidence metric. The likelihood confidence of an action
term
t
j
is computed as follow:
(
t
j
)
={
a
l
1
,
a
l
2
,...,
a
ln
}
, and
Right
(
t
j
)
={
a
r
1
,
a
r
2
,...,
a
rn
}
TermConf
(
t
j
)
=
Like
(
t
j
)/
sup
(
Left
(
t
j
)).
(9.2)
composing a meta-action
m
j
,
we can define the confidence of
m
j
as the weighted sum of its atomic action terms
likelihood confidence where the weights represent atomic action terms likelihood
support. To be more precise, the meta-action confidence
MetaConf
Given the set of atomic action terms
{
t
i
:
1
≤
i
≤
n
}
(
m
j
)
is computed
as follows:
i
=
1
Like
(
t
i
)
·
TermConf
(
t
i
)
MetaConf
(
m
j
)
=
i
=
1
Like
,
(9.3)
(
t
i
)
where
n
is the number of atomic action terms in
m
j
.
Note that some action terms will have the likelihood support below the required
threshold value, therefore, they will not be considered as frequent action terms.
However, those action terms are considered as outliers and it is important to keep
track of them in the meta-actions for objects personalized meta-actions.
9.5 Meta-actions Versus Action Rules
Meta-actions and action rules are similar concepts since they aim at extracting transi-
tion patterns from information systems. However, the meta-action extraction process
extracts a subset of the action terms extracted by the action rule extraction process.
Table 9.2
Meta-actions versus action rules
Action rules
Meta-actions
One objects is one instance
One objects is a set of instances
No instance order
Temporal instance order
Support is minimum support of classification rule
Likelihood is the number of real transitions
Confidence independent probability
Term confidence and execution confidence
Possible transitions
Real transitions
Rules
Collection of action terms
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