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a change of value f
(
x i ) j derived from the transaction s i , j to f
(
x i ) k derived from
the transaction s i , k , for each attribute f
X .
Now, we can use the sets A j , k to build the influence matrix [ 7 , 13 ] covering
all m
F and x i
M . Sets of action terms representing meta-actions in M can be built from
sets of pairs in P
. Depending on the objects' states, some of the atomic action
terms in A j , k may not be triggered by meta-actions. To be more precise, for a given
meta-action m j , only objects x l
(
S
)
X that satisfy the following condition will be
affected:
(
.
This way, by applying the meta-action m on x i we will cover the set of attribute
values
s i , j ,
s i , k )
P
(
S
)
such that F
(
x l )
F
(
x i ) j
= ∅
, where s i , j
= (
x i ,
F
(
x i ) j )
, thus the underlying subset of atomic action terms. This
subset can be seen as an action term t containing a set of atomic actions with the
domain Dom
{
F
(
x l )
F
(
x i ) j }
. Multiple action terms can be formed
this way, however, not all possible action terms are applicable to a given dataset.
The number of possible action terms for each meta-action grows monotonously
with the number of extracted pairs, the attributes' domains sizes, and the number of
transactions for each object in X .
Ultimately, in the worst case scenario every object is different and reacts differ-
ently to each specific meta-action. This might result in a large number of action terms
for each meta-action. Possible conflicts within the same meta-action scope such as
(
(
t
) ={
a
F
:
a
(
x l ) =
a
(
x i ) j }
a
,
a j
a k )
and
(
a
,
a j
a l )
, or non useful action terms such as
(
a
,
a j
a j )
for
a
V a might be extracted. Not all atomic action terms are useful
for all objects; however, it is important to keep a record of the different transitions
for the sake of object personalized meta-actions.
We can evaluate the different action terms composing each given meta-action to
avoid conflicts and use the more appealing ones to the treated object. Similarly the
frequent itemsets used in the Apriori [ 1 ] algorithm, frequent action terms can be
extracted from multiple pairs. Multiple action terms of different sizes can be formed
from the resulting atomic action terms (pairs). Frequent action terms are characterized
by their frequency of occurrence throughout all themeta-action partition of the dataset
(all the meta-action pairs).
F and a j ,
a k ,
a l
9.4.3 Meta-action Evaluation
To evaluate the meta-actions, we need to evaluate the action terms composing them.
A simple evaluation metric consist of the frequency of occurrence (or support) for
each action term. Pairs extracted from the data share common atomic action terms
transitions, thus, they share common action terms. For each action term t j , we define
its likelihood support Like
(
t j )
as:
card { (
rLike
(
t j ) =
s i , k ,
s i , l )
P
(
S
) :
Left
(
t j )
F
(
x i ) k and
(9.1)
x i ) l } ,
Right
(
t j )
F
(
 
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