multilayer perceptron
DESCRIPTION
MULTILAYER PERCEPTRON. Nurochman , Teknik Informatika UIN Sunan Kalijaga Yogyakarta. Review SLP. X1. w 1. Σ. f(y ). w 2. X2. output. activation f unc. Σ x i .w i. w i. X3. weight. Fungsi Aktivasi. Fungsi undak biner (hard limit) Fungsi undak biner (threshold). . - PowerPoint PPT PresentationTRANSCRIPT
MULTILAYER PERCEPTRONNurochman, Teknik Informatika UIN Sunan Kalijaga Yogyakarta
Review SLP
ΣX2
.
.
.
w1
w2
wi
weight
f(y)
Σ xi.wi
activation func
X3
X1
output
Fungsi Aktivasi Fungsi undak biner (hard limit)
Fungsi undak biner (threshold)
Fungsi Aktivasi Fungsi bipolar
Fungsi bipolar dengan threshold
Fungsi Aktivasi Fungsi Linier (identitas)
Fungsi Sigmoid biner
Learning Algorithm Inisialisasi laju pembelajaran (α), nilai
ambang (𝛉), bobot serta bias Menghitung
Menghitung
Learning Algorithm Jika y ≠ target, lakukan update bobot
dan biasWi baru = Wlama + α.t.Xib baru = b lama + α.t
Ulang dari langkah 2 sampai tidak ada update bobot lagi
Problem “OR”X1 X2 net Y, 1 jika net >=1, 0 jika net < 1
1 1 1.1+1.1=2 11 0 1.1+0.1=1 10 1 0.1+1.1=1 10 0 0.1+0.1=0 0
Ternyata BERHASIL mengenali pola
X1
X2
Y
1
1
1
Problem “AND”X1 X2 net Y, 1 jika net >=2, 0 jika net < 2
1 1 1.1+1.1=2 11 0 1.1+0.1=1 00 1 0.1+1.1=1 00 0 0.1+0.1=0 0
Ternyata BERHASIL mengenali pola
X1
X2
Y
2
1
1
Problem “X1 and not(X2)”X1 X2 net Y, 1 jika net >=2, 0 jika net < 2
1 1 1.2+1.-1=1 01 0 1.2+0.-1=2 10 1 0.2+1.-1=-1 00 0 0.2+0.-1=0 0
Ternyata BERHASIL mengenali pola
X1
X2
Y
2
2
-1
HOW ABOUT XOR?
Problem “XOR”X1 X2 Y
1 1 01 0 10 1 10 0 0
GAGAL!
F(1,1) = 0
F(1,0) = 1F(0,0) = 0
F(0,1) = 1
Solusi XOR = (x1 ^ ~x2) V (~x1 ^ x2) Ternyata dibutuhkan sebuah layer
tersembunyiX1
X2
Z1
Z2
Y
2
2
-1-1
1
1
2
2
1
Tabel
Multi-Layer Perceptron MLP is a feedforward neural network with
at least one hidden layer (Li Min Fu) Limitations of Single-Layer Perceptron Neural Network for Nonlinier Pattern
Recognition XOR Problem
Solution for XOR Problem
X1 X2 X1 XOR X2
-1 -1 -1
-1 1 1
1 -1 1
1 1 -1
1
1
-1
-1
x1
x2
Solution from XOR Problem
+1
+1+1
+1-1
-1
x1
x2
-1
0,1
-1
1 if v > 0(v) =
-1 if v 0 is the sign function.
Input to Hidden layer
x1
x2
Net1 f1 Net2 f2
-1 -1 (-1.1+-1.-1) +-1=-1
-1 (-1.-1+-1.1)+-1 = -1
-1
-1 1 (-1.1+1.-1)+-1= -3
-1 (-1.-1+1.1)+-1 = 1
1
1 -1 (1.1+-1.-1) +-1= 1
1 (1.-1+-1.1)+-1 = -3
-1
1 1 (1.1+1.-1)+-1 = -1
-1 (1.-1+1.1)+-1 = -1
-1
Hidden to Output layer
Z1 Z2 Net Y
-1 -1 (-1.1+-1.1) = -1,9 -1
-1 1 (-1.1+1.1) = 0,1 1
1 -1 (1.1+-1.1) = 0,1 1
-1 -1 (-1.1+-1.1) = -1,9 -1
Learning Algorithm Backpropagation Algorithm
It adjusts the weights of the NN in order to minimize the average squared error
Function signalsForward Step
Error signalsBackward Step
BP has two phases Forward pass phase: computes ‘functional
signal’, feedforward propagation of input pattern signals through network
Backward pass phase: computes ‘error signal’, propagates the error backwards through network starting at output units (where the error is the difference between actual and desired output values)
Activation Function Sigmoidal Function
-10 -8 -6 -4 -2 2 4 6 8 10
jv
)( jv 1
Increasing ajave
1
1j)(v
i,...,0
jijv ywmi