1 Introduction
2 Attribute reduction methods
3 Basic notions
\(U{\setminus } A\)
| Temperature | Headache | Weakness | Nausea | Flu |
---|---|---|---|---|---|
1 | Very high | Yes | Yes | No | Yes |
2 | Normal | No | No | No | No |
3 | High | No | No | No | No |
4 | Normal | No | Yes | No | Yes |
5 | Normal | No | Yes | No | No |
6 | High | Yes | No | Yes | Yes |
7 | Very high | No | No | No | No |
8 | Normal | Yes | Yes | Yes | Yes |
4 Horizontal decomposition for attribute reduction
4.1 Horizontal decomposition of information system
4.2 Horizontal decomposition of decision table
5 Data decomposition-based algorithms for attribute reduction
5.1 Attribute reduction algorithms
5.2 Evaluation of algorithms
6 Experiments
Electricity board—5:45781 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 2 | 2.6(4) | 3.30(4) | 3.68(40) |
Time taken | 336.730 | 321.818 | 321.818 | 324.446 |
Ratio | 1 |
0.955
|
0.955
|
0.963
|
Car evolution—7:1728 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 1 | 1(1) | 1.29(3) | 1.55(5) |
Time taken | 0.561 | 0.531 | 0.546 | 0.530 |
Ratio | 1 |
0.95
|
0.97
|
0.94
|
Kingrook vs king (krk)—7:28056 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 1 | 1.5(2) | 1.78(3) | 2.11(6) |
Time taken | 148.003 | 141.228 | 144.754 | 138.731 |
Ratio | 1 |
0.95
|
0.98
|
0.94
|
Pima Indians diabetes—9:768 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 27 | 25.4(32) | 23.96(34) | 20.38(31) |
Time taken | 0.187 | 0.203 | 0.234 | 0.533 |
Ratio | 1 | 1.09 | 1.25 | 2.85 |
Nursery—9:12960 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 1 | 1(1) | 2(1.22) | 4(1.53) |
Time taken | 33.976 | 32.104 | 32.261 | 33.087 |
Ratio | 1 |
0.94
|
0.95
|
0.97
|
Shuttle—10:43500 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 1 | 1(1) | 1(1) | 1.11(4) |
Time taken | 422.215 | 421.514 | 417.783 | 420.015 |
Ratio | 1 |
0.998
|
0.990
|
0.995
|
Breast cancer Wisconsin—11:699 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 2 | 3.4(10) | 2.35(10) | 1.58(13) |
Time taken | 0.140 | 0.156 | 0.156 | 0.172 |
Ratio | 1 | 1.11 | 1.11 | 1.23 |
Wine—14:178 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 128 | 68.3(80) | 47.45(73) | 19.0(51) |
Time taken | 0.125 | 0.218 | 0.327 | 0.374 |
Ratio | 1 | 1.74 | 2.62 | 2.99 |
Australian credit approval—15:690 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 13 | 71.5(129) | 88.8(154) | 74.1(141) |
Time taken | 0.219 | 0.609 | 2.917 | 9.328 |
Ratio | 1 | 2.78 | 13.32 | 42.6 |
Adult—15:32561 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 2 | 4.6(13) | 11.8(28) | 20.32(56) |
Time taken | 392.777 | 401.981 | 385.292 | 407.436 |
Ratio | 1 | 1.02 |
0.98
| 1.04 |
Meta-data—22:528 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 33 | 21.2(33) | 22.27(41) | 18.29(39) |
Time taken | 0.147 | 0.183 | 0.187 | 0.281 |
Ratio | 1 | 1.24 | 1.27 | 1.91 |
Mushroom—23:8124 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 1 | 39.4(323) | 154.9(1226) | 216.5(1124) |
Time taken | 32.558 | 43.368 | 172.568 | 929.894 |
Ratio | 1 | 1.33 | 5.30 | 28.56 |
Trains—33:10 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 3588 | 152.4(381) | 13.1(24) | – |
Time taken | 26.471 | 22.451 | 26.541 | – |
Ratio | 1 |
0.85
| 1.003 | – |
Turkiye student evaluation—33:5820 | ||||
No. mid. subt. | 1 | 4 | 10 | 20* |
No. reducts | 1 | 98.2(724) | 36.25(287) | 61.1(2205) |
Time taken | 20.795 | 21.855 | 22.261 | 84.365 |
Ratio | 1 | 1.05 | 1.07 | 4.06 |
Sonar, mines vs. rocks—61:208 | ||||
No. mid. subt. | 1 | 4 | 10 | 25 |
No. reducts | 1714 | 567.1(721) | 174.38(311) | 68.48(114) |
Time taken | 259.475 | 403.355 | 357.556 | 321.059 |
Ratio | 1 | 1.55 |
1.38
|
1.24
|