www.kdd.uncc.edu
College of Computing and Informatics
University of North Carolina, Charlotte
RSES – reducts and
discretization of attributes
presented by
Zbigniew W. Ras
University of North Carolina, Charlotte, NC &
Warsaw University of Technology, Poland
Information System
a
b
c
d
f
x1
x2
0
0
L
R
0
1
L
L
0
1
x3
x4
0
0
L
R
0
1
L
L
0
1
x5
1
R
0
L
2
x6
1
R
0
L
2
x7
2
S
2
H
3
x8
2
S
2
H
3
Discernibility Matrix
x1
x2
x3
x4
x5
x6
x7
x8
bc
bc
bc
bc
ab
ac
ab
ac
ab
ac
ab
ac
abcd abcd abcd abcd abcd abcd
abcd abcd abcd abcd abcd abcd
x1
x2
x3
x4
x5
x6
x7
x8
Discernibility Function:
f(a, b, c, d) = (b + c) (a + b) (a + b + c + d) (a + c) =(b + c) (a + b) (a + c) =
(ba + bb + ca + cb) (a + c) = (b + ca) (a + c)
ba + bc + ca
(b=L)  (f=0);
(a=0)*(b=R)  (f=1);
Possible coverings: {b, a}, {c, a}, {c, b}
……
Discretization of numerical attributes
X
x1
x2
x3
x4
x5
x6
x7
a
0.8
1
1.3
1.4
1.4
1.6
1.3
b
2
0.5
3
1
2
3
1
d
1
0
0
1
0
1
1
Va = [0, 2), Vb = [0, 4)
p1 p2 p3
p4
Dom(a) = {0.8, 1, 1.3, 1.4, 1.6},
G(x1,x2)=p1+q1+q2
G(x1,x3)=p1+p2+q3
G(x1,x5)=p1+p2+p3
G(x2,x4)=p2+p3+q1
G(x2,x6)=p2+p3+p4+q1+q2+q3
G(x2,x7)=p2+q1
G(x3,x4)=p3+q2+q3
G(x3,x6)=p3+p4
G(x3,x7)=q2+q3
G(x4,x5)=q2
G(x5,x6)=p4+q3
G(x5,x7)=p3+q2
x1,x3
x1,x5
x2,x4
x2,x7
x3,x6
x5,x6
q1 q2 q3
Dom(b) = {0.5, 1,
2, 3}
P1 P
2
1 1
1 1
P
3
P4 Q1 Q2 Q3
1
1
1
1
1
1
1
1
(x1, x2)
(x1, x3)
(x1, x5)
(x4, x2)
(x4, x3)
(x4, x5)
(x6, x2)
(x6, x3)
(x6, x5)
(x7, x2)
(x7, x3)
(x7, x5)
new
p(1, a)
1
1
1
0
0
0
0
0
0
0
0
0
0
p(2, a)
0
1
1
1
0
0
1
0
0
1
0
0
0
p(3, a)
0
0
1
1
1
0
1
1
0
0
0
1
0
p(4, a)
0
0
0
0
0
0
1
1
1
0
0
0
0
p(1, b)
1
0
0
1
0
0
1
0
0
1
0
0
0
p(2, b)
1
0
0
0
1
1
1
0
0
0
1
1
0
p(3, b)
0
1
0
0
1
0
1
0
1
0
1
0
0
d*
1
1
1
1
1
1
1
1
1
1
1
1
0
Step 1.
Choose a column from B with the maximal number of occurrences of 1’s.
Step 2.
Delete from B the column chosen in Step 2 and all rows marked in this
column by 1.
Step 3.
If B is non-empty go to step 2 else Stop.
Questions?
Thank You