multilayer perceptron

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MULTILAYER PERCEPTRON Nurochman, Teknik Informatika UIN Sunan Kalijaga Yogyakarta

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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 Presentation

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Page 1: MULTILAYER  PERCEPTRON

MULTILAYER PERCEPTRONNurochman, Teknik Informatika UIN Sunan Kalijaga Yogyakarta

Page 2: MULTILAYER  PERCEPTRON

Review SLP

ΣX2

.

.

.

w1

w2

wi

weight

f(y)

Σ xi.wi

activation func

X3

X1

output

Page 3: MULTILAYER  PERCEPTRON

Fungsi Aktivasi Fungsi undak biner (hard limit)

Fungsi undak biner (threshold)

Page 4: MULTILAYER  PERCEPTRON

Fungsi Aktivasi Fungsi bipolar

Fungsi bipolar dengan threshold

Page 5: MULTILAYER  PERCEPTRON

Fungsi Aktivasi Fungsi Linier (identitas)

Fungsi Sigmoid biner

Page 6: MULTILAYER  PERCEPTRON

Learning Algorithm Inisialisasi laju pembelajaran (α), nilai

ambang (𝛉), bobot serta bias Menghitung

Menghitung

Page 7: MULTILAYER  PERCEPTRON

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

Page 8: MULTILAYER  PERCEPTRON

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

Page 9: MULTILAYER  PERCEPTRON

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

Page 10: MULTILAYER  PERCEPTRON

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

Page 11: MULTILAYER  PERCEPTRON

HOW ABOUT XOR?

Page 12: MULTILAYER  PERCEPTRON

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

Page 13: MULTILAYER  PERCEPTRON

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

Page 14: MULTILAYER  PERCEPTRON

Tabel

Page 15: MULTILAYER  PERCEPTRON

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

Page 16: MULTILAYER  PERCEPTRON

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

Page 17: MULTILAYER  PERCEPTRON

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.

Page 18: MULTILAYER  PERCEPTRON

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

Page 19: MULTILAYER  PERCEPTRON

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

Page 20: MULTILAYER  PERCEPTRON

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

Page 21: MULTILAYER  PERCEPTRON

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)

Page 22: MULTILAYER  PERCEPTRON

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