1. ( )
yokkuns:
2010/04/20
1

2. AGENDA
• 2
–
–
– JS ,JΣ
•
•
2

3. •
•
• KL
3

4. KL
4

5. KL
5

6. KL
2
6

7. 7

8. 8

9. • ωi Si
def ∑
Si = (x − mi)(x − mi)t (1)
x∈χi
• SW SB
def
SW = S∑ S2
1+ ∑ (2)
= (x − mi)(x − mi)t (3)
i=1,2 x∈χi
def ∑
SB = ni(mi − m)(mi − m)t (4)
i=1,2
n1 n2
= (m1 − m)(m2 − m)t (5)
n
9

10. 1
• d 1 A(d, 1) x A
y
y = Atx (6)
∼
• mi
∼ 1 ∑ 1 ∑ t
mi = y= Ax (7)
ni y∈Y ni x∈χi
i
10

11. 1
∼ ∼
• SW SB
∼ ∼ ∼
SW = S1 + S2 (8)
∑ ∑ ∼
= (y − mi)2 (9)
i=1,2 y∈Yi
= AtSW A (10)
∼ ∑ ∼
SB = ni(mi − m)2 (11)
i=1,2
n1n2 ∼
= (mi − m)2 (12)
n
= AtSB A (13)
11

12. • =
1
∼
• SW
∼
SB A
• JS (A)
∼ ∼
def SB n1n2 (mi − m)2
JS (A) = ∼ = · ∼2 ∼2
(14)
SW n n1σ1 n2σ2
AtSB A
= (15)
AtSW A
12

13. • JS (A) A CA
max AtSB A s.t.AtSW A = 1 (16)
A
•
L(A, λ) = AtSB A − λAtSW A (17)
∂L(A, λ)
= SB A − λSW A = 0 (18)
∂A
(19)
•
−1
SW SB A = λA (20)
13