Question

Artificial Neural Network

Using the Perceptron learning rule, Find the weights required to perform the following classifications: 1. Vectors (1,1,1,1) and (0,1,0,0) are members of the class, and therefore have target value 1. 2. Vectors (1,1,1,0) and (1,0,0,1) are not members of the class, and have target value 0. Use a learning rate of 1, 0 =0.3, and starting weights of 0. Using each of the training vectors as input, test the responses of the net.

Answer 1

x1=(1,1,1,1)   y1=1
x2=(0,1,0,0)   y2=1
x3=(1,1,1,0)   y3=0
x4=(1,0,0,1)   y4=0

x0=1(bias)
let w0=0,w1=0,w2=0,w3=0,w4=0

z=x0*w0+x1*w1+x2*w2+x3*w3+x4*w4
threshould(t)=0

wi=wi+(O-y)Input
t=t-(O-y)
for x1
   z=1*0+1*0+1*0+1*0+1*0=0!>0 so y=0 and actual output(O) is 1
   so increare w's and decrease t

   after iter 1:
       w0=1,w1=1,w2=1,w3=1,w4=1
       t=-1
   z=5>-1 so y=1 and O also 1

for x2
   z=2>-1 so y=1 and O is 1 so no change
   w0=1,w1=1,w2=1,w3=1,w4=1
   t=-1

for x3
   z=4>-1 so y=1 and O is 0 so reduce weight and increase t

   w0=1,w1=0,w2=0,w3=0,w4=1
   t=1
   z=1!>1 so y=0 and O is 0
for x4
   z=2>1 so y=1 and O is 0 so reduce weight and increase t

   w0=0,w1=-1,w2=0,w3=0,w4=0
   t=2
   z=-1!>2 so y=0 and O is 0

for x1
   z=-1!>2 so y=0 and O is 1 so increase w's and reduce t
   w0=1,w1=0,w2=1,w3=1,w4=1
   t=1

finally the weights are
w0=-1,w1=-1,w2=1,w3=0,w4=1
t=-1
for x1: 0>-1 true so y=1 and y1 also 1
for x2: 0>-1 true so y=1 and y2 also 1
for x3: -1>-1 false so y=0 and y3 also 0
for x4:-1>-1 false so y=0 and y4 also 0