Noviembre 29 2014
• • • •
2n
⊕
Y = X 0 ⊕ X 1
Y = X 0 ⊕ X 1 ⊕ X 2 X 0 X 1
Y
X 0
X 1
X 2
X 2
X 3
X 1
X 2
X 1
X 2
X 3 = X 1 ⊕ X 2
X 4 X 4 Y
X 0 X 1 X 2 X 3
X 4
Y
•
X 0
X 1
X 2
X 3
X 4
Y
•
X 0 , X 1 , X 2 ,X 3
X 4
• X 0 • X 1 X 2
X 3
• X 4
p(X i = x i , S i = s i ) > 0
xi y si
p(Y = y |X i = x i , S i = s i ) = p (Y = y |S i = s i )
S i
si
p(X i = x i , S i = s i ) > 0
p(Y = y |X i = x i , S i = s i ) = p (Y = y |S i = s i )
X 0 S 0 = { X 1 , X 2 , X 3 , X 4 }
S 0 = { 0, 1, 1, 0}
p(Y = 1 |X 0 = 0, S 0 = { 0, 1, 1, 0})= 1 p(Y = 1|S 0 = { 0, 1, 1, 0}) = 0, 5
X 0 X 1
S 1 = { X 0 , X 2 , X 3 , X 4 }
S 1 = { 1, 1, 0, 0}
p(Y = 1 |X 1 = 0, S 1 = { 1, 1, 0, 0}) = 0
p(Y = 1|S 1 = { 1, 1, 0, 0}) = 0, 5
X 1 X 2
S 2 = { X 0 , X 1 , X 3 , X 4 }
S 2 = { 1, 1, 0, 1}
p(Y = 1 |X 2 = 0, S 2 = { 1, 1, 0, 1}) = 0
p(Y = 1|S 2 = { 1, 1, 0, 1}) = 0, 5
X 2 X 3
S 3 = { X 0 , X 1 , X 2 , X 4 }
S 3 = { 1, 1, 0, 1}
p(Y = 1 |X 3 = 1, S 3 = { 1, 1, 0, 1}) = 0
p(Y = 1|S 3 = { 1, 1, 0, 1}) = 0, 5
X 3 X 3
X 1 X 2
X 4 X 4 S 4 = { 0, 0, 0, 0} p(Y = 1 |X 4 = 0, S 4 = { 0, 0, 0, 0})= 0 p(Y = 1|S 4 = { 0, 0, 0, 0}) = 0
S 4 = { X 0 , X 1 , X 2 , X 3 } Y
X 0
X 1
X 2
X 3
S 4
p(Y = y |X i = x i , S i = s i )
p(Y = y |S i = s i )
{0, 0, 0, 0} {0, 0, 1, 1} {0, 1, 0, 1} {0, 1, 1, 0} {1, 0, 0, 0} {1, 0, 1, 1} {1, 1, 0, 1} {1, 1, 1, 0} X 4
X 4 X 4
{X 0 , X 1 , X 2 , X 3 , X 4 , Y }
• •
•
αk J =
J
1 yh yk αh αk (xh ∗ xk + λδ hk ) − αk ≤ α k ≤ C...and.. αk yk = 0 2 hk
k
{x1 , x2 , x3 ,...,xk ,..xl
{y1 , y2 , y3 ,...,yk ,..yl
X k xh ∗ xk yk δ hk λ C
δ hk = 1
k
h = k δ hk = 0
rzc =
rzc k rzi rii
•
•
•
kr zi
k + k − (k − 1)rii
(x1 ,...,xn )
(x1 ,...,xn )
xi =
d
ak,i ek , d ≤ d
k =1
S = E [xi xT i ] E d =
1 2
d
i+d +1 λk
S ek
d
S
ai,k E [xi xT i ]
ek xi xT i
E d
λk
ek.
Consistency S = 1 −
J | D i | − | M i | i=0
IN
S J
S
Di M i IN
C
S C best
C best ,
C best
• •
X 0 , X 1 , X 2 , X 3 , X 4 X 0 , X 3 , X 2 , X 1 , X 4 X 0 , X 1 , X 3 X 0 , X 3 , X 1 , X 2 X 0 , X 1 , X 3 X 0 , X 1 , X 2 , X 3 X 0 , X 2 X 0 , X 1 , X 2 X 0 , X 3 , X 1 , X 2 , X 4 X 0 , X 3 X 0 , X 3 , X 1 , X 2 X 0 , X 3 X 0 , X 3 , X 1 , X 2 X 0 , X 2 X 0 , X 2 , X 1 , X 3 X 0 , X 3 X 0 , X 3 , X 1 X 0 , X 3 X 0 , X 3 , X 1 , X 2 X 0 , X 1 , X 4 X 0 , X 4 , X 1 , X 2 X 0 , X 3 X 0 , X 3 , X 1 X 0 , X 3 X 0 , X 3 , X 1 , X 2 X 0 , X 1 , X 4 X 0 , X 4 , X 1 , X 2 , X 3
•
X 4
•
X 0 X 1 X 3
X 1
X 2
X 2
•
•
X 0 X 1
•
X 2
Referencias
