Sebelum kita bahas perhitungan pencarian bobotnya, alangkah lebih baik kita mengenal dulu apa itu Perceptron. Perceptron merupakan feedforward neural network yang sederhana yang diperkenalkan oleh Rosenblatt (1958), Minsky and Papert (1969/1988),Fausett (1994). Biasanya digunakan untuk mengklasifikasikan suatu pola tipe tertentu yang sering dikenal dengan pemisahan secara linear. Pada dasarnya perceptron pada jaringan syaraf dengan satu lapisan memiliki bobot yang dapat diatur. Dapat digunakan dalam kasus untuk mengenali fungsi logika AND, OR, ANDNOT, ORNOT dengan masukan dan keluaran bipolar.Baik, saya kira cukup perkenalannya. Sekarang kita akan bahas bagaimana penyelesaiannya untuk fungsi ANDNOT (untuk penyelesaiannya fungsi lainnya, akan saya bahas jika ada request dari temen-temen)
X1
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X2
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X1 AND NOT(X2)
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1
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1
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-1
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1
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0
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1
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0
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1
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-1
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0
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0
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-1
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α=1 , +teta = 0.2, -teta = -0.2
Epoch 1
x1
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x2
|
1
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NotYin
|
f(Yin)
|
t
|
ΔW1
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ΔW2
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Δb
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W1
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W2
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b
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0
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0
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0
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|||||||||
1
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1
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1
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0
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0
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-1
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-1
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-1
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-1
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-1
|
-1
|
-1
|
1
|
0
|
1
|
-2
|
-1
|
1
|
1
|
0
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1
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0
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-1
|
0
|
0
|
1
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1
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-1
|
-1
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-1
|
0
|
0
|
0
|
0
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-1
|
0
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0
|
0
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1
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0
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0
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-1
|
0
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0
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-1
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0
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-1
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-1
|
Yin = x1.W1 + x2.W2 + b Yin
=(1*0)+(1*0)+0 Yin =
0
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= 0
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*1 ΔW1
= -1
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = -1
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= -1
W1 = W1(n-1) + ΔW1 W1=-1+-1 W1
= -1
W2 = W2(n-1) + ΔW2 W2=-1+-1 W2
= -1
b = b(n-1) + Δb b=-1+-1 b =
-1
Yin = x1.W1 + x2.W2 + b Yin
=(1*-1)+(0*-1)+-1 Yin =
-2
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*1*1 ΔW1 = 1
if f(Yin)=1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*1*0
ΔW2 =
0
if f(Yin)=1, then Δb=0 else Δb=α.t.1 Δb=1*1*1 Δb = 1
W1 = W1(n-1) + ΔW1 W1=0+1 W1
= 0
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=0+1 b
= 0
Yin = x1.W1 + x2.W2 + b Yin
=(0*0)+(1*-1)+0 Yin
= -1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=0+0 W1
= 0
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=0+0 b
= 0
Yin = x1.W1 + x2.W2 + b Yin
=(0*0)+(0*-1)+0 Yin
= 0
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= 0
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*0
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= -1
W1 = W1(n-1) + ΔW1 W1=0+0 W1
= 0
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=-1+-1 b =
-1
Epoch 2
x1
|
x2
|
1
|
NotYin
|
f(Yin)
|
t
|
ΔW1
|
ΔW2
|
Δb
|
W1
|
W2
|
b
|
0
|
-1
|
-1
|
|||||||||
1
|
1
|
1
|
-2
|
-1
|
-1
|
0
|
0
|
0
|
0
|
-1
|
-1
|
1
|
0
|
1
|
-1
|
-1
|
1
|
1
|
0
|
1
|
1
|
-1
|
0
|
0
|
1
|
1
|
-1
|
-1
|
-1
|
0
|
0
|
0
|
1
|
-1
|
0
|
0
|
0
|
1
|
0
|
0
|
-1
|
0
|
0
|
-1
|
1
|
-1
|
-1
|
Yin = x1.W1 + x2.W2 + b Yin
=(1*0)+(1*-1)+-1 Yin =
-2
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*1 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=0+0 W1
= 0
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=-1+0 b
= -1
Yin = x1.W1 + x2.W2 + b Yin
=(1*0)+(0*-1)+-1 Yin =
-1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*1*1 ΔW1
= 1
if f(Yin)=1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*1*0
ΔW2 =
0
if f(Yin)=1, then Δb=0 else Δb=α.t.1 Δb=1*1*1 Δb = 1
W1 = W1(n-1) + ΔW1 W1=1+1 W1
= 1
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=0+1 b
= 0
Yin = x1.W1 + x2.W2 + b Yin
=(0*1)+(1*-1)+0 Yin
= -1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=1+0 W1
= 1
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=0+0 b
= 0
Yin = x1.W1 + x2.W2 + b Yin
=(0*1)+(0*-1)+0 Yin
= 0
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= 0
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*0
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= -1
W1 = W1(n-1) + ΔW1 W1=1+0 W1
= 1
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=-1+-1 b =
-1
Epoch 3
x1
|
x2
|
1
|
NotYin
|
f(Yin)
|
t
|
ΔW1
|
ΔW2
|
Δb
|
W1
|
W2
|
b
|
1
|
-1
|
-1
|
|||||||||
1
|
1
|
1
|
-1
|
-1
|
-1
|
0
|
0
|
0
|
1
|
-1
|
-1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
2
|
-1
|
0
|
0
|
1
|
1
|
-1
|
-1
|
-1
|
0
|
0
|
0
|
2
|
-1
|
0
|
0
|
0
|
1
|
0
|
0
|
-1
|
0
|
0
|
-1
|
2
|
-1
|
-1
|
Yin = x1.W1 + x2.W2 + b Yin
=(1*1)+(1*-1)+-1 Yin =
-1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*1 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=1+0 W1
= 1
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 = -1
b = b(n-1) + Δb b=-1+0 b
= -1
Yin = x1.W1 + x2.W2 + b Yin
=(1*1)+(0*-1)+-1 Yin = 0
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= 0
if f(Yin)=1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*1*1 ΔW1
= 1
if f(Yin)=1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*1*0
ΔW2 =
0
if f(Yin)=1, then Δb=0 else Δb=α.t.1 Δb=1*1*1 Δb = 1
W1 = W1(n-1) + ΔW1 W1=2+1 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=0+1 b
= 0
Yin = x1.W1 + x2.W2 + b Yin
=(0*2)+(1*-1)+0 Yin
= -1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb = 0
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=0+0 b
= 0
Yin = x1.W1 + x2.W2 + b Yin
=(0*2)+(0*-1)+0 Yin
= 0
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= 0
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*0
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= -1
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-1+0 W2 =
-1
b = b(n-1) + Δb b=-1+-1 b =
-1
Epoch 4
x1
|
x2
|
1
|
NotYin
|
f(Yin)
|
t
|
ΔW1
|
ΔW2
|
Δb
|
W1
|
W2
|
b
|
2
|
-1
|
-1
|
|||||||||
1
|
1
|
1
|
0
|
0
|
-1
|
-1
|
-1
|
-1
|
1
|
-2
|
-2
|
1
|
0
|
1
|
-1
|
-1
|
1
|
1
|
0
|
1
|
2
|
-2
|
-1
|
0
|
1
|
1
|
-3
|
-1
|
-1
|
0
|
0
|
0
|
2
|
-2
|
-1
|
0
|
0
|
1
|
-1
|
-1
|
-1
|
0
|
0
|
0
|
2
|
-2
|
-1
|
Yin = x1.W1 + x2.W2 + b Yin
=(1*2)+(1*-1)+-1 Yin = 0
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= 0
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*1 ΔW1
= -1
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = -1
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= -1
W1 = W1(n-1) + ΔW1 W1=1+-1 W1 =
1
W2 = W2(n-1) + ΔW2 W2=-2+-1 W2
= -2
b = b(n-1) + Δb b=-2+-1 b =
-2
Yin = x1.W1 + x2.W2 + b Yin
=(1*1)+(0*-2)+-2 Yin =
-1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*1*1 ΔW1 = 1
if f(Yin)=1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*1*0
ΔW2 =
0
if f(Yin)=1, then Δb=0 else Δb=α.t.1 Δb=1*1*1 Δb = 1
W1 = W1(n-1) + ΔW1 W1=2+1 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-2+0 W2 =
-2
b = b(n-1) + Δb b=-1+1 b
= -1
Yin = x1.W1 + x2.W2 + b Yin
=(0*2)+(1*-2)+-1 Yin =
-3
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-2+0 W2 =
-2
b = b(n-1) + Δb b=-1+0 b
= -1
Yin = x1.W1 + x2.W2 + b Yin
=(0*2)+(0*-2)+-1 Yin =
-1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*0
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-2+0 W2 =
-2
b = b(n-1) + Δb b=-1+0 b
= -1
Epoch 5
x1
|
x2
|
1
|
NotYin
|
f(Yin)
|
t
|
ΔW1
|
ΔW2
|
Δb
|
W1
|
W2
|
b
|
2
|
-2
|
-1
|
|||||||||
1
|
1
|
1
|
-1
|
-1
|
-1
|
0
|
0
|
0
|
2
|
-2
|
-1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
2
|
-2
|
-1
|
0
|
1
|
1
|
-3
|
-1
|
-1
|
0
|
0
|
0
|
2
|
-2
|
-1
|
0
|
0
|
1
|
-1
|
-1
|
-1
|
0
|
0
|
0
|
2
|
-2
|
-1
|
Yin = x1.W1 + x2.W2 + b Yin
=(1*2)+(1*-2)+-1 Yin =
-1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*1 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-2+0 W2 =
-2
b = b(n-1) + Δb b=-1+0 b
= -1
Yin = x1.W1 + x2.W2 + b Yin
=(1*2)+(0*-2)+-1 Yin = 1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= 1
if f(Yin)=1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*1*1 ΔW1 = 0
if f(Yin)=1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*1*0
ΔW2 =
0
if f(Yin)=1, then Δb=0 else Δb=α.t.1 Δb=1*1*1 Δb = 0
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-2+0 W2 =
-2
b = b(n-1) + Δb b=-1+0 b
= -1
Yin = x1.W1 + x2.W2 + b Yin
=(0*2)+(1*-2)+-1 Yin =
-3
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*1
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-2+0 W2 =
-2
b = b(n-1) + Δb b=-1+0 b
= -1
Yin = x1.W1 + x2.W2 + b Yin
=(0*2)+(0*-2)+-1 Yin =
-1
if Yin>0.2, then f(Yin)=1 else f(Yin)=-1 f(Yin)
= -1
if f(Yin)=-1, then ΔW1=0 else ΔW1=α.t.x1 ΔW1=1*-1*0 ΔW1
= 0
if f(Yin)=-1, then ΔW2=0 else ΔW2=α.t.x2 ΔW2=1*-1*0
ΔW2 = 0
if f(Yin)=-1, then Δb=0 else Δb=α.t.1 Δb=1*-1*1 Δb
= 0
W1 = W1(n-1) + ΔW1 W1=2+0 W1
= 2
W2 = W2(n-1) + ΔW2 W2=-2+0 W2 =
-2
b = b(n-1) + Δb b=-1+0 b
= -1
Yin = x1.W1
+ x2.W2 + 1.b
Yin = X1.2 + X2.-2
+ -1
Yin= 2X1 - 2X2
- 1
Fungsi Matematika:
·
2X1 - 2X2
– 1 >= 0.2
2X1 - 2X2 – 1.2 = 0
X1 =0.6 X2
= 0
X1 =0 X2 = -0.6
·
2X1 - 2X2
– 1 <= -0.2
2X1 - 2X2 – 0.8 = 0
X1 =0.4 X2
= 0
X1 =0 X2
= -0.4
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