Information Technology Reference
In-Depth Information
An introduction to feature selection is presented in [
17
]. Recently two topics were
published [
18
,
24
], summarizing research in this area. There is active research on
feature selection in statistics, data mining, and soft computing.
The main objective of this chapter is to compare, in terms of an error rate, rule
complexity, and time complexity of two approaches: an approach to rule induction
based on feature selection with another approach to rule induction, based on the
LEM2 algorithm, without any feature selection. In the former approach computations
are conducted on the entire attributes, so it is also called
global
[
14
]. To be more
specific, for every attribute a corresponding partition on the set of all cases, implied by
the indiscernibility relation [
26
-
28
] is computed and feature selection is conducted
by computation on such partitions. On the other hand, the LEM2 algorithm works
on attribute values, instead on entire attributes, so it is called
local
[
14
]. The search
space of the LEM2 algorithm is the set of all blocks of attribute-value pairs. A block
of an attribute-value pair
is the set of all cases with the value of
a
equal to
v
.
A preliminary version of this chapter was presented at IPMU 2012, the 14th
International Conference on Information Processing andManagement of Uncertainty
in Knowledge-Based Systems, Catania, Italy, July 9-13, 2012 [
15
] (Table
8.1
).
(
a
,
v
)
Table 8.1
Acronyms and symbols used in the chapter and their meaning
Acronym or symbol
Meaning
A
Set of all attributes
appr
(
X
)
Lower approximation of
X
appr
(
X
)
Upper approximation of
X
B
Subset of the set
A
of all attributes
B
∗
Partition on
U
defined by
B
C
Concept of the data sets
d
Decision
}
∗
{
d
Partition on
U
, the set of all concepts
G
Goal of the LEM2
IND
(
B
)
Indiscernibility relation of
B
LEM
1
Learning from Examples Module version 1
LEM
2
Learning from Examples Module version 2
LERS
Learning from Examples based on Rough Sets data mining system
t
Attribute-value pair
(
a
,
v
)
T
Complex, i.e., a set of attribute-value pairs
T
(
G
)
Set of attribute-value pairs relevant with
G
Local covering
T
U
Universe, the set of all cases of data set
x
Element of
U
X
Subset of
U
|
X
|
Cardinality of the set
X
y
Element of
U
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