Databases Reference
In-Depth Information
each
R
j
. With regards to both stages of rule weighting and rule re-ordering,
each rule ordering mechanism can be described in more detail as follows:
•
CSA:
The CSA rule ordering mechanism is based on the well-established
“Support-Confidence” framework (see Sect. 2.1). It does not assign an ad-
ditional weighting score to each
R
j
∈R
in its rule weighting stage, but
simply gathers the values of confidence and support, and the size of the
rule antecedent to “express” a weighting score for each
R
j
∈R
.Inthe
rule re-ordering stage, CSA generally sorts the original
in a descending
order based on the value of confidence of each
R
j
. For these rules in
R
that
share a common value of confidence, CSA sorts them in a descending order
based on their support value. Furthermore for these rules in
R
that share
common values for both confidence and support, CSA sorts them in an
ascending order based on their size of the rule antecedent. In this chapter,
the “pure confidence” approach is applied as a simplified version of the
CSA rule ordering mechanism, which sorts the original
R
R
in a descending
order based on the value of confidence of each
R
j
only.
•
WRA:
The use of WRA can be found in [35], where this technique is
used to determine an expected accuracy for each generated CR. In its
rule weighting stage, WRA assigns a weighting score to each
R
j
∈R
.
The calculation of the value of
R
j
, confirmed in [15], is:
wra
(
R
j
)=
support
(
R
j
.antecedent
)
(
confidence
(
R
j
)-
support
(
R
j
.consequent
). In
the rule re-ordering stage the original
×
is simply sorted in a descending
order based on the assigned
wra
value of each
R
j
.
R
•
Laplace Accuracy:
The use of the
Laplace expected error estimate
[10]
can be found in [53]. The principle of applying this rule ordering mech-
anism is similar to WRA. The calculation of the
Laplace
value of
R
j
is:
Laplace
(
R
j
)=
support
(
R
j
.antecedent
∪
R
j
.consequent
)+1
support
(
R
j
.antecedent
+
|C|
)
,where
|
C
|
is the
size function of the set
C
.
•
χ
2
Testing: χ
2
Testing is a well known technique in statistics, which can be
used to determine whether two variables are independent of one another.
In
χ
2
Testing a set of observed values (
O
) is compared against a set of
expected values (
E
) - values that would be estimated if there were no
associative relationship between the variables. The value of
χ
2
is calculated
as:
i
=1
(
O
i
−
E
i
)
2
,where
n
is the number of observed/expected values,
which is always 4 in CARM. If the
χ
2
E
i
value between two variables (the
antecedent and consequent of
R
j
∈R
) above a given threshold value (for
CMAR the chosen threshold is 3.8415), thus it can be concluded that there
is a relation between the rule antecedent and consequent, otherwise there
is not a relation. After assigning a
χ
2
value to each
R
j
∈R
, it can be used
to re-order the
R
in a descending basis.
•
ACS:
The ACS rule ordering mechanism is a variation of CSA. It takes the
size of the rule antecedent as its major factor (using a descending order)
followed by the rule confidence and support values respectively. This rule
ordering mechanism ensures that “specific rules have a higher precedence
than more general rules” [15].
