Transcript Chapter2

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Neuron Model
and
Network Architectures
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Biological Inspiration
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Neuron Model
a1~an為輸入向量的各個分量
w1~wn為神經元各個突觸的權值
b為偏差
f為傳遞函數，通常為非線性函數。
例如：hardlim(n) ，n正為1，其餘0
t為神經元輸出
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Notation
Scalars-small italic letters：a,b,c
Vectors-small bold nonitalic letters：a,b,c
Matrices-capital BOLD nonitalic letters：A,B,C
Input-p,p,P
Weight-w,w,W
Bias-b,b
Output-a,a,a(t)
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Single-Input Neuron
例1：w=3,p=2 and b=-1.5 then
a=f(3(2)-1.5)=f(4.5)
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Transfer Functions
a=0 n<0
a=1 n>=0
例2：w=3, p=2 and b=-1.5 then
a=hardlim(3(2)-1.5)=hardlim(4.5)=1
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Transfer Functions
例3：w=3, p=2 and b=-1.5 then
a=purelin(3(2)-1.5)=purelin(4.5)=4.5
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Transfer Functions
例4：w=3, p=2 and b=-1.5 then
a=logsig(3(2)-1.5)=logsig(4.5)=
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Transfer Functions
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0<=a<=1
-1<=a<=1
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Multiple-Input Neuron
Neuron With R Inputs
Abbreviated Notation
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Example P2.3
Given a two-input neuron with the following parameters: b=1.2,
W= [ 3 2 ] and p= [ -5 6 ]T , calculate the neuron output for
the following transfer functions:
i. A symmetrical hard limit transfer function
ii. A saturating linear transfer function
iii. A hyperbolic tangent sigmoid(tansig) transfer function
i. a=hardlims(-1.8)= -1
ii. a=satlin(-1.8)= 0
iii. a=tansig(-1.8)=
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Layer of S Neurons
Layer of S Neurons
R Input
S Output
i.e.,R≠S
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Abbreviated Notation
w 1, 1 w 1, 2  w 1, R
W=
w 2, 1 w 2, 2  w 2, R
w S, 1 w S, 2  w S, R
p1
p=
p2
pR
b1
b=
b2
bS
a1
a=
a2
aS
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Multiple Layers of Neurons
Three-Layer Network
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Abbreviated Notation
Hidden Layers
Output Layer
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Delays and Integrators
a(0)=a(0)
a(1)=u(0)
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Recurrent Network
a 1 = satlins Wa 0 + b = satlins Wp + b 
a2 = satlins Wa 1 + b 
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