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PRESENTED BY:
ER.Abhishek k. upadhyay
ECE(REGULAR),2015
6/4/2015 1
 A neural network is a processing device, whose design was
inspired by the design and functioning of human brain and
their components.
 Different neural network algorithms are used for
recognizing the pattern.
 Various algorithms differ in their learning mechanism.
 All learning methods used for adaptive neural networks
can be classified into two major categories:
 Supervised learning
 Unsupervised learning
6/4/2015 2
 Its capability for solving complex pattern recognition
problems:-
 Noise in weights
 Noise in inputs
 Loss of connections
 Missing information and adding information.
6/4/2015 3
 The primary function of which is to retrieve in a pattern
stored in memory, when an incomplete or noisy version of
that pattern is presented.
 This is a two layer classifier of binary bipolar vectors.
 The first layer of hamming network itself is capable of
selecting the stored class that is at minimum HD value to
the test vector presented at the input.
 The second layer MAXNET only suppresses outputs.
6/4/2015 4
6/4/2015 5
 The hamming network is of the feed forward type. The
number of output neurons in this part equals the number
of classes.
 The strongest response of a neuron of this layer indicated
the minimum HD value between the input vector and the
class this neuron represents.
 The second layer is MAXNET, which operates as a recurrent
network. It involves both excitatory and inhibitory
connections.
6/4/2015 6
6/4/2015 7
 The purpose of the layer is to compute, in a feed forward
manner, the values of (n-HD).
 Where HD is the hamming distance between the search
argument and the encoded class prototype vector.
 For the Hamming net, we have input vector X
p classes => p neurons for output
output vector Y = [y1,……yp]
6/4/2015 8
 for any output neuron ,m, m=1, ……p, we have
Wm = [wm1, wm2,……wmn]t and
m=1,2,……p
to be the weights between input X and each output
neuron.
 Also, assuming that for each class m, one has the
prototype vector S(m) as the standard to be matched.
6/4/2015 9
 For classifying p classes, one can say the m’th output is 1 if
and only if
 output for the classifier are
XtS(1), XtS(2),…XtS(m),…XtS(p)
 So when X= S(m), the m’th output is n and other outputs
are smaller than n.
X= S(m) W(m) =S(m)
=> happens only
6/4/2015 10
Xt S(m) = (n - HD(X , S(m)) ) - HD(X , S(m))
∴½ XtS(m) = n/2 – HD(X , S(m))
So the weight matrix:
WH=½S















)()(
2
)(
1
)2()2(
2
)2(
1
)1()1(
2
)1(
1
2
1
p
n
pp
n
n
H
SSS
SSS
SSS
W




6/4/2015 11
 By giving a fixed bias n/2 to the input
then
netm = ½XtS(m) + n/2 for m=1,2,……p
or
netm = n - HD(X , S(m))
 To scale the input 0~n to 0~1 down, one can apply
transfer function as
f(netm) = 1/n(netm) for m=1,2,…..p
6/4/2015 12
6/4/2015 13
 So for the node with the the highest output means that
the node has smallest HD between input and prototype
vectors S(1)……S(m)
i.e.
f(netm) = 1
for other nodes
f(netm) < 1
 The purpose of MAXNET is to let max{ y1,……yp }
equal to 1 and let others equal to 0.
6/4/2015 14
6/4/2015 15
 So
ε is bounded by 0<ε<1/p and
 ε: lateral interaction coefficient
)(
1
1
1
1
pp
MW

































6/4/2015 16
 And
 So the transfer function






0
00
)(
netnet
net
netf
6/4/2015 17
 kk
k
M
k
netfY
YWnet


1
 Each entry of the updated vector decreases at the k’th
recursion step under the MAXNET update algorithm,
with the largest entry decreasing slowest.
6/4/2015 18
 Step 1: Consider that patterns to classified are a1, a2 …
ap,each pattern is n dimensional. The weights connecting
inputs to the neuron of hamming network is given by
weight matrix.















pmpp
n
n
H
aaa
aaa
aaa
W




21
22121
11211
2
1
6/4/2015 19
 Step2: n-dimensional input vector x is presented to the
input.
 Step3: Net input of each neuron of hamming network is
netm = ½XtS(m) + n/2 for m=1,2,……p
Where n/2 is fixed bias applied to the input of each neuron
of this layer.
 Step 4: Out put of each neuron of first layer is,
f(netm) =1/n( netm) for m=1,2,…..p
6/4/2015 20
 Step 5: Output of hamming network is applied as input to
MAXNET
y0=f(netm)
 Step 6: Weights connecting neurons of hamming
network and MAXNET is taken as,
)(
1
1
1
1
pp
MW

































6/4/2015 21
 Where ε must be bounded 0< ε <1/p. the quantity ε can be
called the literal interaction coefficient. Dimension of WM
is p×p.
 Step 7: The output of MAXNET is calculated as,
 k=1, 2, 3…… denotes the no of iterations.






0
00
)(
netnet
net
netf
 k1k
k
M
k
netfY
YWnet



6/4/2015 22
 Ex: To have a Hamming Net for classifying C , I , T
then
S(1) = [ 1 1 1 1 -1 -1 1 1 1 ]t
S(2) = [ -1 1 -1 -1 1 -1 -1 1 -1 ]t
S(3) = [ 1 1 1 -1 1 -1 -1 1 -1 ]t
 So,
6/4/2015 23














111111111
111111111
111111111
HW
6/4/2015 24
 For
 And
6/4/2015 25
22
1 n
XWnet H 
 
Y
netf
t








9
5
9
3
9
7
 
 t
t
net
X
537
111111111


 Input to MAXNET and select =0.2 < 1/3(=1/p)
 So,
 And
6/4/2015 26




















1
5
1
5
1
5
1
1
5
1
5
1
5
1
1
MW
 kk
k
M
k
netfY
YWnet


1
 K=o
6/4/2015 27
 















































333.0
067.0
599.0
333.0
067.0
599.0
555.0
333.0
777.0
12.02.0
2.012.0
2.02.01
01
0
netfY
o
net
 K=1
 K=2
6/4/2015 28
  t
t
Y
net
2
0
1
120.00520.0
120.0120.0520.0














  t
t
Y
net
3
0
2
096.00480.0
096.014.0480.0














 K=3
 The result computed by the network after four
recurrences indicates the vector x presented at i/p for
mini hamming distance has been at the smallest HD
from s1.
 So, it represents the distorted character C.
6/4/2015 29
  t
t
Y
net
4
7
0
3
00461.0
10115.0461.0











 


 Noise is introduced in the input by adding random
numbers.
 Hamming Network and MaxNet network recognizes
correctly all the stored strings even after introducing noise
at the time of testing.
6/4/2015 30
 In the network, neurons are interconnected and every
interconnection has some interconnecting coefficient
called weight.
 If some of these weights are equated to zero then how it is
going to effect the classification or recognition.
 The number of connections that can be removed such that
the network performance is not affected.
6/4/2015 31
 Missing information means some of the on pixels in
pattern grid are made off.
 For the algorithm, how many information we can miss so
that the strings can be recognized correctly varies from
string to string.
 The number of pixels that can be switched off for all the
stored strings in algorithm.
6/4/2015 32
 Adding information means some of the off pixels in the
pattern grid are made on.
 The number of pixels that can be made on for all the strings
that can be stored in networks.
6/4/2015 33
 The network architecture is very simple.
 This network is a counter part of Hopfield auto associative
network.
 The advantage of this network is that it involves less
number of neurons and less number of connections in
comparison to its counter part.
 There is no capacity limitation.
6/4/2015 34
 The hamming network retrieves only the closest class index
and not the entire prototype vector.
 It is not able to restore any of the key patterns. It provides
passive classification only.
 This network does not have any mechanism for data
restoration.
 It’s not to restore distorted pattern.
6/4/2015 35
 Jacek M. Zurada, “Introduction to artificial Neural
Systems”, Jaico Publication House. New Delhi, INDIA
 Amit Kumar Gupta, Yash Pal Singh, “Analysis of Hamming
Network and MAXNET of Neural Network method in the
String Recognition”, IEEE ,2011.
 C.M. Bishop, Neural Networks for Pattern Recognition,
Oxford University Press, Oxford, 2003.
6/4/2015 36
6/4/2015 37

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Nural network ER.Abhishek k. upadhyay

  • 1. PRESENTED BY: ER.Abhishek k. upadhyay ECE(REGULAR),2015 6/4/2015 1
  • 2.  A neural network is a processing device, whose design was inspired by the design and functioning of human brain and their components.  Different neural network algorithms are used for recognizing the pattern.  Various algorithms differ in their learning mechanism.  All learning methods used for adaptive neural networks can be classified into two major categories:  Supervised learning  Unsupervised learning 6/4/2015 2
  • 3.  Its capability for solving complex pattern recognition problems:-  Noise in weights  Noise in inputs  Loss of connections  Missing information and adding information. 6/4/2015 3
  • 4.  The primary function of which is to retrieve in a pattern stored in memory, when an incomplete or noisy version of that pattern is presented.  This is a two layer classifier of binary bipolar vectors.  The first layer of hamming network itself is capable of selecting the stored class that is at minimum HD value to the test vector presented at the input.  The second layer MAXNET only suppresses outputs. 6/4/2015 4
  • 6.  The hamming network is of the feed forward type. The number of output neurons in this part equals the number of classes.  The strongest response of a neuron of this layer indicated the minimum HD value between the input vector and the class this neuron represents.  The second layer is MAXNET, which operates as a recurrent network. It involves both excitatory and inhibitory connections. 6/4/2015 6
  • 8.  The purpose of the layer is to compute, in a feed forward manner, the values of (n-HD).  Where HD is the hamming distance between the search argument and the encoded class prototype vector.  For the Hamming net, we have input vector X p classes => p neurons for output output vector Y = [y1,……yp] 6/4/2015 8
  • 9.  for any output neuron ,m, m=1, ……p, we have Wm = [wm1, wm2,……wmn]t and m=1,2,……p to be the weights between input X and each output neuron.  Also, assuming that for each class m, one has the prototype vector S(m) as the standard to be matched. 6/4/2015 9
  • 10.  For classifying p classes, one can say the m’th output is 1 if and only if  output for the classifier are XtS(1), XtS(2),…XtS(m),…XtS(p)  So when X= S(m), the m’th output is n and other outputs are smaller than n. X= S(m) W(m) =S(m) => happens only 6/4/2015 10
  • 11. Xt S(m) = (n - HD(X , S(m)) ) - HD(X , S(m)) ∴½ XtS(m) = n/2 – HD(X , S(m)) So the weight matrix: WH=½S                )()( 2 )( 1 )2()2( 2 )2( 1 )1()1( 2 )1( 1 2 1 p n pp n n H SSS SSS SSS W     6/4/2015 11
  • 12.  By giving a fixed bias n/2 to the input then netm = ½XtS(m) + n/2 for m=1,2,……p or netm = n - HD(X , S(m))  To scale the input 0~n to 0~1 down, one can apply transfer function as f(netm) = 1/n(netm) for m=1,2,…..p 6/4/2015 12
  • 14.  So for the node with the the highest output means that the node has smallest HD between input and prototype vectors S(1)……S(m) i.e. f(netm) = 1 for other nodes f(netm) < 1  The purpose of MAXNET is to let max{ y1,……yp } equal to 1 and let others equal to 0. 6/4/2015 14
  • 16.  So ε is bounded by 0<ε<1/p and  ε: lateral interaction coefficient )( 1 1 1 1 pp MW                                  6/4/2015 16
  • 17.  And  So the transfer function       0 00 )( netnet net netf 6/4/2015 17  kk k M k netfY YWnet   1
  • 18.  Each entry of the updated vector decreases at the k’th recursion step under the MAXNET update algorithm, with the largest entry decreasing slowest. 6/4/2015 18
  • 19.  Step 1: Consider that patterns to classified are a1, a2 … ap,each pattern is n dimensional. The weights connecting inputs to the neuron of hamming network is given by weight matrix.                pmpp n n H aaa aaa aaa W     21 22121 11211 2 1 6/4/2015 19
  • 20.  Step2: n-dimensional input vector x is presented to the input.  Step3: Net input of each neuron of hamming network is netm = ½XtS(m) + n/2 for m=1,2,……p Where n/2 is fixed bias applied to the input of each neuron of this layer.  Step 4: Out put of each neuron of first layer is, f(netm) =1/n( netm) for m=1,2,…..p 6/4/2015 20
  • 21.  Step 5: Output of hamming network is applied as input to MAXNET y0=f(netm)  Step 6: Weights connecting neurons of hamming network and MAXNET is taken as, )( 1 1 1 1 pp MW                                  6/4/2015 21
  • 22.  Where ε must be bounded 0< ε <1/p. the quantity ε can be called the literal interaction coefficient. Dimension of WM is p×p.  Step 7: The output of MAXNET is calculated as,  k=1, 2, 3…… denotes the no of iterations.       0 00 )( netnet net netf  k1k k M k netfY YWnet    6/4/2015 22
  • 23.  Ex: To have a Hamming Net for classifying C , I , T then S(1) = [ 1 1 1 1 -1 -1 1 1 1 ]t S(2) = [ -1 1 -1 -1 1 -1 -1 1 -1 ]t S(3) = [ 1 1 1 -1 1 -1 -1 1 -1 ]t  So, 6/4/2015 23               111111111 111111111 111111111 HW
  • 25.  For  And 6/4/2015 25 22 1 n XWnet H    Y netf t         9 5 9 3 9 7    t t net X 537 111111111  
  • 26.  Input to MAXNET and select =0.2 < 1/3(=1/p)  So,  And 6/4/2015 26                     1 5 1 5 1 5 1 1 5 1 5 1 5 1 1 MW  kk k M k netfY YWnet   1
  • 27.  K=o 6/4/2015 27                                                  333.0 067.0 599.0 333.0 067.0 599.0 555.0 333.0 777.0 12.02.0 2.012.0 2.02.01 01 0 netfY o net
  • 28.  K=1  K=2 6/4/2015 28   t t Y net 2 0 1 120.00520.0 120.0120.0520.0                 t t Y net 3 0 2 096.00480.0 096.014.0480.0              
  • 29.  K=3  The result computed by the network after four recurrences indicates the vector x presented at i/p for mini hamming distance has been at the smallest HD from s1.  So, it represents the distorted character C. 6/4/2015 29   t t Y net 4 7 0 3 00461.0 10115.0461.0               
  • 30.  Noise is introduced in the input by adding random numbers.  Hamming Network and MaxNet network recognizes correctly all the stored strings even after introducing noise at the time of testing. 6/4/2015 30
  • 31.  In the network, neurons are interconnected and every interconnection has some interconnecting coefficient called weight.  If some of these weights are equated to zero then how it is going to effect the classification or recognition.  The number of connections that can be removed such that the network performance is not affected. 6/4/2015 31
  • 32.  Missing information means some of the on pixels in pattern grid are made off.  For the algorithm, how many information we can miss so that the strings can be recognized correctly varies from string to string.  The number of pixels that can be switched off for all the stored strings in algorithm. 6/4/2015 32
  • 33.  Adding information means some of the off pixels in the pattern grid are made on.  The number of pixels that can be made on for all the strings that can be stored in networks. 6/4/2015 33
  • 34.  The network architecture is very simple.  This network is a counter part of Hopfield auto associative network.  The advantage of this network is that it involves less number of neurons and less number of connections in comparison to its counter part.  There is no capacity limitation. 6/4/2015 34
  • 35.  The hamming network retrieves only the closest class index and not the entire prototype vector.  It is not able to restore any of the key patterns. It provides passive classification only.  This network does not have any mechanism for data restoration.  It’s not to restore distorted pattern. 6/4/2015 35
  • 36.  Jacek M. Zurada, “Introduction to artificial Neural Systems”, Jaico Publication House. New Delhi, INDIA  Amit Kumar Gupta, Yash Pal Singh, “Analysis of Hamming Network and MAXNET of Neural Network method in the String Recognition”, IEEE ,2011.  C.M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, Oxford, 2003. 6/4/2015 36