Databases Reference
In-Depth Information
Definition 2.
Let c
A
(
R
j
)
denote the contribution of each CAR R
j
∈R
for
class A, which represents how significantly R
j
determines A.
The calculation of
c
A
(
R
j
) is given as follows:
c
A
(
R
j
)=
|R
j
|
h
=1
c
A
(
Item
h
∈
R
j
).
3.2 Some Definitions
Definition 3.
If c
A
(
Item
h
)
<ε, we recognise Item
h
D
TR
as a light-
weighted item for class A, where ε is a user-defined constant and
0
∈
1
.
We use I
(
A
)=
{Item
1
,Item
2
,...,Item
|I
(
A
)
|−
1
,Item
|I
(
A
)
|
} to denote the
su
cient set of light-weighted items for A, identified in D
TR
.
≤
ε
≤
Definition 4.
If a CAR R
j
∈R
significantly satisfies the following inequality,
c
A
(
R
j
)
>
|I
(
A
)
|
I
(
A
))
, where the contribution of R
j
for class
A is significantly greater than the sum of the contributions of all light-weighted
items for class A, we recognise R
j
as a heavy-weighted rule for A.Weuse
R
(
A
)=
c
A
(
Item
h
∈
h
=1
R
1
,R
2
,...,R
t−
1
,R
t
}
{
to denote the set of selected heavy-weighted
rules for A, identified in
R
.In
R
, we always select the top-t heavy-weighted
rules to construct
R
(
A
)
, where integer t is a user-defined constant.
Definition 5.
We recognise an item Item
h
∈
D
TR
as a heavy-weighted rule-
R
j
∈R
(
A
))
.WeuseI
(
A
)=
Item
1
,Item
2
,
item for class A if Item
h
∈
(
∃
{
...,Item
|I
(
A
)
|−
1
,Item
|I
(
A
)
|
}
to denote the su
cient set of heavy-weighted
rule-items for A, identified in D
TR
.
Definition 6.
If a CAR R
j
∈R
does not contain any item Item
h
∈
I
(
A
)
, we recognise R
j
as a noisy rule for class A.Weuse
R
(
A
)=
R
1
,R
2
,...,R
k
−
1
,R
k
}
{
to denote the su
cient set of noisy rules for A, iden-
tified in R.
Definition 7.
We recognise an item Item
h
∈
D
TR
as a noisy rule-
R
j
∈R
(
A
))
.WeuseI
(
A
)=
item for class A if Item
h
∈
(
∃
Item
1
,Item
2
,...,Item
|I
(
A
)
|−
1
,Item
{
|I
(
A
)
|
}
to denote the su
cient set
of noisy rule-items for A, identified in D
TR
.
Definition 8.
If a CAR
(
R
j
∈R
)
/∈R
(
A
)
, we recognise R
j
as a potential
significant rule for class A.WeuseR
(
A
)=
{R
1
,R
2
,...,R
k−
1
,R
k
} to
denote the su
cient set of potential significant rules for class A, identified in
R
R−R
(
A
)
, where integer k
as
≥
t (See Definition 4).
∈R
(
A
)
satisfies the following inequality,
Definition 9.
If a CAR
(
R
j
∈R
)
c
A
(
R
j
)
>
|I
(
A
)
|
I
(
A
))
, where the contribution of R
j
to class
A is greater than the sum of the contributions of all noisy rule-items for class
A, we recognise R
j
as a significant rule for A. We say there are at most
c
A
(
Item
h
∈
h
=1
k
, where integer k is a user-defined constant
significant rules for A in
R
≤
k.
