1. RSES – reducts and discretization of attributes presented by Zbigniew W. Ras University of North Carolina, Charlotte, NC & Warsaw University of Technology, Poland College of Computing and Informatics University of North Carolina, Charlotte www.kdd.uncc.edu

2. abcdf x10L0L0 x20R1L1 x30L0L0 x40R1L1 x51R0L2 x61R0L2 x72S2H3 x82S2H3 x1 x2bc x3-bc x4bc- x5abacabac x6abacabac- x7abcd x8abcd - x1x2x3x4x5x6x7x8 Discernibility Matrix Information System 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 Possible coverings:{b, a}, {c, a},{c, b} (b=L)  (f=0); (a=0)*(b=R)  (f=1); ……

3. Discretization of numerical attributes Xabd x10.821 x210.50 x31.330 x41.411 x51.420 x61.631 x71.311 p1 p2 p3 p4 q1 q2 q3 Dom(a) = {0.8, 1, 1.3, 1.4, 1.6}, Dom(b) = {0.5, 1, 2, 3} Va = [0, 2), Vb = [0, 4) 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 P1P2P2 P3P3 P4Q1Q2Q3 x1,x311 1 x1,x5111 x2,x4 x2,x7 1 1 x3,x6 11 x5,x6 1 1

4. p(1, a)p(2, a)p(3, a)p(4, a)p(1, b)p(2, b)p(3, b)d* (x1, x2)10001101 (x1, x3)11000011 (x1, x5)11100001 (x4, x2)01101001 (x4, x3)00100111 (x4, x5)00000101 (x6, x2)01111111 (x6, x3)00110001 (x6, x5)00010011 (x7, x2)01001001 (x7, x3)00000111 (x7, x5)00100101 new00000000 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.

5. Thank You Questions?