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ABA1
NEURAL NETWORKSNEURAL NETWORKS
..
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ABA3
) (
)Information Processing(
)Parallel(
""
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)10 12 (
10000
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)Artificial Neuron(
""
)Processing Unit( )Perceptron (
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+
W 1W 2
W n
X1
X2
Xn
.
.
.
Y
Otherwise
xW If n
iii
>=1
1
0
=
:
) "OR () "AND(" ) "NAND(
" ) "NOR (
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ABA8
:
W i new = W i old + a (O desired O) x i
:
W i =O =x i =a =
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ABA9
") "OR (
1
x1 x2 O desired
0 0 0
0 1 1
1 0 1
1 1 1
W 1
W 2
x1
x2
O
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ABA10
:
W1 new = W1 old + (O desired O) x1
W2 new = W2 old + (O desired O) x2
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ABA12
)Classification(
(Separation)
"" Boundary
X 2
(0,0) (1,0)X 1
1
00
0(0,1)
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ABA13
" "XOR
!!!!!
X 2
(0,0) (1,0)X 1
0
10
1(0,1)
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ABA14
" "
X 2
(0,0) (1,0)X 1
0
10
1(0,1)
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ABA15
)Feed forward networks(
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ABA17
1
2
3
x1
x2
x3
4
5
6
7
8
W 14
W 15
W 24
W34
W 35
W 46
W 58
O 1
O 2
O 3
W 25
W48
W 57
W 47
W 56
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ABA18
""
)Threshold
(
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ABA19
Supervised Neural Networks
)Weights (
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ABA20
" "
) Error Back Propagation(
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ABA21
)Feedforward Networks(
:
" " " "
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ABA22
Activation Functions
:
:
: )Differentiation(
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ABA23
)Activation Function (
)( ) (
:
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ABA24
f (x)
x
x
e
x f +=
1
1)(
1
f (x)=xf (x)
1
x
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ABA25
x2 = 0.2
w 22=6
x1 = 0.1
w 11=3w 12=4
w 21=5
w 10=7
w 20=8
x2 = 0.1
w 22=6
+
+
+
x1 = 0.1w 11=3
w 12=4 w 21=5
1.62
f
f /
1.6
1.3
w 10=7
w 20=8 o=1.622
79.03.111 = e
83.06.11
1 = e
?
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ABA26
)Training Algorithm(
)Back propagation(
) ( .
" ) "Least Mean Squares (
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ABA27
:
[ ])x(f 1)x(f
dx)x(df
xe1
1)x(
+=f
:
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ABA28
:
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ABA29
t (Target) : O (Output) :
f (Activ. Func.) : (Learning Rate) :
W (Weight) :
(Error signal) :
)Subscripts( .
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ABA30
i j kw ij w jk
O ko jo i..
.
.
..
.
.
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ABA31
:
:
j jO jk Wk N
:
)k N(1
1k O f
=kNe
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ABA32
: )( :
:
.
:
)k N()k Ok t(k ' f
)k O1(k O)k Ok t(k
jWW k jk jk
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ABA33
: :
:
k
k jk W jO1 j j
i jijWijW
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ABA34
1
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ABA35
x 2
W 22
x 1
W 11
W 12 W 21h 1
h 2
Input Layer( i )
Output (O )
Hidden( h )
W 10
W 20
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ABA37
:
h i1 = h i2 =
h o1 =
h o2 =
N =
O =
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ABA38
:
h i1 = W 11 x1 + W 21 x2= (1) (0) + (0) (0)= 0
h i2 = W 12 x1 + W 22 x2= (0) (0) + (1) (0)= 0
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ABA39
1ihe1
11Oh +
=
5.00e1
1=
+=
2ihe1
12Oh +
=
5.00e1
1=+
=
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ABA40
:
:
N = W 10 h O1 + W 20 h O2
= (1) (0.5) + (1) (0.5) = 1
1e1
1
Ne1
1O
=
=
= 0.73106
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ABA41
:
:
O1OOtO = (0-0.73106) (0.73106) (1-0.73106)
= -0.14373
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ABA42
1OhO10W10W = 1 + (1) (-.14373) (0.5) = 0. 92813
2OhO20W20W = 1 + (1) (-.14373) (0.5) = 0. 92813
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ABA43
. :
O10W1Oh11Ohh1 = (0.5) (1-0.5) (.92813) (-0.14373) = -0.03335
O20W2Oh12Ohh 2 = (0.5) (1-0.5) (0.92813) (-0.14373)
= -0.03335
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ABA45
x 1 x 2 t W 11 W 12 W 21 W 22 W 10 W 20
0 0 0 1 0 0 1 0.92813 0.92813
:x
1 = 0 , x 2 = 1 , t = 1
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ABA46
:
x 1 x 2 t W 1 1 W 1 2 W 2 1 W 2 2 W 1 0 W 2 0
0 1 1 1 0 0 .0 1 0 5 4 1 .0 0 8 3 8 0 .9 5 0 3 0 .9 6 0 5 6
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ABA47
W 11 W 12 W 21 W 22 W 10 W 20
-3.5402 4.0244 -3.5248 4.5814 -11.9103 4.6940
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ABA48
x 1 x 2 Target (t) O utput (O )
0 0 0 0.0264
0 1 1 0.9867
1 0 1 0.9863
1 1 1 0.9908
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ABA49
:
. :
)Overfitting( )Underfitting(
)Normalization( )Learning Rate(
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ABA50
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ABA51
) Early Stopping(.
:
)Training(
)Validation( )Testing(
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ABA53
:
)Trial and Error(
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ABA54
MATLAB
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ABA55
Normalization .
:
: : ) 1 1-(
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ABA56
:
Learning Rate
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ABA57
) (
1
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ABA58
) ( ) (
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