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based on the probabilities of one attribute value occurring together with the value
of the second attribute, and for the classification task the second attribute will cor-
respond to a special attribute in the dataset defined as class. The ST measure for the
capability of input attribute
at
i
in predicting the class attribute
Y
is defined in [
54
]
as follows.
c
=
1
r
=
1
P
(
rc
)
+
r
=
1
c
=
1
P
(
rc
)
−
r
=
1
P
(
r
+
)
−
c
=
1
P
(
+
c
)
2
P
(
+
c
)
2
P
(
r
+
)
2
2
(10.1)
Ta u
(
at
i
,
Y
)
=
2
−
r
=
1
P
(
r
+
)
−
c
=
1
P
(
+
c
)
2
2
The higher values of the ST measure would indicate better discriminating criteria
(features) for the class that is to be predicted in the domain. As performed in [
15
], the
attributes are ranked according to their decreasing ST values and a relevance cut-off
point is chosen at and below which all attributes are considered as irrelevant and are
discarded. The relevance cut-off was selected based on the significant difference (less
than half of the previous value in the ranking) between the ST values in decreasing
order. This will prevent the generation of rules which would then need to be discarded
when found that they were comprised of some irrelevant attributes. In accordance
with [
5
] we have found that mutual information typically ranks attributes with more
values higher than the ST measure does.
Chi-square
: A natural way to express the dependence between antecedent and
the consequence of an association rule is the correlation based on the chi-square
test for independence [
7
]. The chi-square test is defined as follows: For a given
D
tr
, the occurrence of
at
i
where
at
i
∈
AT
,(
i
=
(
1
,...,
|
AT
|
)
is independent of the
occurrence of
y
r
∈
; otherwise
at
i
and
y
r
are dependent
and correlated. The correlation between
at
i
and
y
r
Y
if
P
(
at
i
∪
y
r
)
=
P
(
at
i
)
P
(
y
r
)
Y
is measured using Eq.
10.2
.
For a given lift measure [
40
] based on Eq.
10.2
, the chi-square
∈
2
statistic value was
utilised to determine whether the correlation is statistically significant.
ˇ
P
(
at
i
∪
y
r
)
lift
(
at
i
,
y
r
)
=
(10.2)
P
(
at
1
)
P
(
y
r
)
Hence, the chi-square test discards any
fA
k
∈
F
(
A
)
for which
∃
at
i
contained in
x
2
value is not significant for
y
of
x
Y
(correlation analysis in Eq.
10.2
).
Logistic Regression
: Another form of statistical analysis applied was the logistic
regression. The relationship between the antecedent and consequent in association
rule mining can be presented as a relationship between a target variable and the input
variables in logistic regression. The following is the definition of the logistic regres-
sion model involved in the framework. For a given
D
tr
, several logistic regression
models were developed based on
ln
ₒ
y
,the
ˇ
∈
(
Y
)
=
ʲ
0
+
ʲ
1
at
1
+
ʲ
2
at
2
+···+
ʲ
|
AT
|
at
|
+
e
,
|
AT
where
ln
are the coef-
ficients of the input attributes
at
i
,
e
is the error variable and
Y
the dichotomous class
attribute. The coefficient
(
Y
)
is the natural logarithm of the odds ratio,
ʲ
0
,ʲ
1
,...,ʲ
|
AT
|
ʲ
i
of
at
i
is determined based on the log likelihood value
giveninEq.
10.3
, where
at
i
val
r
denotes the value of attribute
at
i
occurring in record
r
.
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