Information Technology Reference
In-Depth Information
T
(
G
)
:= {
t
|[
t
]∩
G
=∅}
;
(
)
:=
(
)
−
T
G
T
G
T
;
end
{while}
for
each
t
∈
T
do
if
[
T
−{
t
}] ↆ
B
then
T
:=
T
−{
t
}
;
T
:=
T
∪{
T
}
;
G
:=
B
−∪
T
∈
T
[
T
]
;
end
{while};
for
each
T
do
if
S
∈
T
−{
T
}
[
∈
T
S
]=
B
then
T
:=
T
−{
T
}
;
end
{algorithm}.
With the same assumptions as for the algorithm for computing a single global
covering, the time complexity of the algorithm for computing a single local covering
is also
O
mn
2
m
2
n
2
(
)
for symbolic attributes and
O
(
)
for attributes with the number
of values depending on
m
.
The LERS data mining system also includes the LEM2 algorithm.
The first step of the algorithm LEM2 is to compute all attribute-value pair blocks.
For Table
8.2
, these blocks are
[
(
Temperature
,
very
_
high
)
]={
2
,
3
}
,
[
(
Temperature
,
high
)
]={
1
,
5
}
,
[
(
Temperature
,
normal
)
]={
4
,
6
}
,
[
(
Headache
,
yes
)
]={
1
,
3
,
6
}
,
[
(
Headache
,
no
)
]={
2
,
4
,
5
}
,
[
(
Nausea
,
no
)
]={
1
,
1
,
3
,
4
}
,
}
.
Let us induce rules for the concept {5, 6}. It is immediately clear that {(
Nausea
,
yes
)} is the only required minimal complex and that the local covering consists of
only this single minimal complex.
The corresponding rule set, induced by LEM2, contains just one rule
(
[
(
Nausea
,
yes
)
]={
5
,
6
).
Obviously, in general, rule sets induced by LEM2 are simpler than rule sets
induced by LEM1 from the same data sets. This observation is confirmed by our
experiments.
Nausea
,
yes
)
ₒ
(
Flu
,
maybe
8.4 Inconsistent Data
An example of the inconsistent data set is presented in Table
8.3
. In inconsistent data
some cases may conflict with each other. Conflicting cases have the same attribute
values yet different decision values. In Table
8.3
cases 1 and 7 are conflicting. A
level of consistency
is the ratio of the cardinality of the set of all cases not involved
in any conflict to the cardinality of
U
. For the data set from Table
8.3
,the
level of
consistency
is
7
= 71.4%.
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