4. (1/3)
•
•
•
•
•

5. (2/3)
• (
Classification, Pattern Recognition)
•
•
• A

6. (3/3)
• (Clustering)
•
• A B
• A B
• (Association Rules)
•
• A B
•

9. •
•
9

10. •
K
L
10

11. •
•
•
•
•
T T’
Yes No Yes No
(A) (B) 11

12. • T v∈T cost(v) v T
.
{cost(x) | x ∈ T is leaf}
5.4. 133
X1
X2 X3
1 0 1 X4
: 2 2 2
1 0
3 3 12

13. 13

14. 5.1
EXACT COVER BY 3-SET
• NP NP
• NP NP EXACT EXACT COVER BY 3-SET
COVER BY 3-SET
EXACT COVER BY 3-SET
• EXACT COVER BY 3-SET
5.2 3 X 3 X
S = {T 1, T 2, ...} S1 ⊂ S
NP
(1) ∪{T |T ∈ S1 } = X
5.4. X S1 135
134 5
(2) i=j Ti ∩ Tj = φ S 1
5.4 EXACT COVER BY 3-SET
1 2 3 {{1, 4, 7}, {2, 3, 5}, {6, 8, 9}}
X EXACT COVER
BY 3-SET 4 5 6 EXACT COVER
: NP BY 3-SET
7 8 9
14

15. BY 3-SET
•: NP
•
•
X 1 |X|
• X Y = {y1 , y2 , ..., y|X| } |X| 0 Y
t X Y Y = {y1 , y2 , . . . X |X| }
,y 1 Y
• t 0X Y X 1 Y 0
1 t∈X
t[A] =
0 t∈Y
X 3 T1 , T 2 , . . .
1 0 yi
1
1 t ∈ Ti 1 t = yi

16. 0 t∈Y
•X X 3
3
T1 , T 2 , . . . T1 , T 2 , . . .
1 1 0 0 yi
• yi 1 1
1 t ∈ Ti 1 t = yi
t[Ti ] = , t[yi ] =
0 t ∈ Ti 0 t = yi
•
Ti yi
•
• 2
• Ti
9 3 5.5(A)
• 5.5(B)

17. •
• |X|
|X| |X|
1 + 2 + ··· + +
3 3
•
• EXACT COVER BY 3-SET
136 EXACT COVER BY 3-SET5
: :
Y T1 T2 T3
yi yi
T1
|Y | = |X| 9
5.6(A) 1 T2
1 T3
1 + 2 + · · · + |X| + |X|1 0
(A) (B)

18. 5.6(A)
• Ti yi yi yi
|Y| = |X|
• 1 + 2 + · · · + |X| + |X|
• 2 1 + 2 + ··· +
|X| |X|
+
3 3
• EXACT COVER BY 3-SET
EXACT COVER BY 3-SET
1 + 2 + · · · + |X|/3 + |X|/3
NP
5.4. 137
y1
5.4.2 0 y2
y1 y2 y3 NP
0
y9
0 1
(A) (B)

19. 19

20. T T’
Yes No Yes No
(A) (B)
20

21. S = {(x1 , c1 ), (x2 , c2 ), . . . , (xN , cN )}
H(C) = −p log2 p − p× log2 p×
p p×
p
21

22. • 4 6
p = , p× =
10 10
• H(C) = −p log2 p − p× log2 p×
4 4 6 6
= − log2 − log2 = 0.971
10 10 10 10
22

23. •
30
YES NO
C: 2 2 4
× 2 4 6
4 6 10 23

24. T1: 30
YES NO
C: 2 2 4
× 2 4 6
4 6 10
2 2 2 2
H(C | T1 = Yes) = − log2 − log2 = 1.0
4 4 4 4
2 2 4 4
H(C | T1 = No) = − log2 − log2 = 0.918
6 6 6 6
•
4 6
H(C | T1 ) = H(C | T1 = Yes) + H(C | T1 = No) = 0.951
10 10
24

25. • T I(T)
I(T ) = H(C) − H(C | T )
•
I(T1 ) = H(C) − H(C | T1 ) = 0.971 − 0.951 = 0.020
•
I(T2 ) = 0.420, I(T3 ) = 0.091, I(T4 ) = 0.420
• T2
T2
• T4
T2
25

26. T2:
Yes No
•
•
•
•

27. • Yes
4 4 2 2
H(C) = − log2 − log2 = 0.918
6 6 6 6
T1 4 2 2 2 2
H(C | T1 ) = − log2 − log2
6 4 4 4 4
2 2 2
− log2
6 2 2
= 0.667
I(T1 ) = 0.918 − 0.667 = 0.251
I(T3 ) = 0, I(T4 ) = 0.918
T4 27

28. •

29. •
•
• naive bayes
•
•
•
•
•
•
•
• 29

30. •
•
•
• ID3
2
•
•
• CART (Classification And Regression Tree) C4.5
30

31. • CART
• 2
•
•
• C4.5
•
•
•
•
•
•
Forest
31

32. (10/21)
• sesejun+dm10@sel.is.ocha.ac.jp
•
• 11/2( )
•
• http://togodb.sel.is.ocha.ac.jp/ 22
2010
32

33. 33