ASSIGNMENT-2
SET-1
1. A neuron with 4 inputs has the weight vector w = [1 2 3 4]t . The activation function is linear,
that is, the activation function is given by f(net) = 2 *net. If the input veCtor is X = [5 6 7 8] ,
then find the output of the neuron.
Net =1*5+2*6+3*7+4*8=70
F(net)=2*net=140
(2)
2. A single neuron network using f(net) = sgn(net) has been trained using the pairs of (Xj,di)as
given below :
XI = [1 -2 3 -1]t dl = -1
X2 = [0 -1 2 -1]t d2 = 1
X3 = [-2 0 -3 -1]t, d3 =-1
The final weights obtained using the perceptron rule are W4 = [3 2 6 1]'
Knowing that correction has been performed in each step for c=l, determine the following
weights:
(a) W3,W2,WI by backtracking the training.
(5)
(b) W5,W6,W7 obtained for steps 4,5,6 of training by reusing the sequence (Xt. dt), (X2, d2),
(X3, d3)
(5)
X1 X2
X3
X4
D
Net F(net) do
-2
3
-1
-1
W1 W2 W3 W4
1
0
2
-1
-1
4
-4
1
Dw1 Dw2
Dw3
Dw4
-1
2
-1
1
-1
2
0
-1
0
-3
-1
-1
3
2
6
1
-2
3
-1
-1
16
1
-2
1
6
0
3
-2
4
-6
2
-1
2
-1
1
-9
-1
2
1
4
4
1
0
-2
4
-2
0
-3
-1
-1
-15
-1
0
1
4
4
1
0
0
0
0
1
0
-2
1
0
-2
3. Determine the weights after one iteration for Hebbian learning of a single neuron network
starting with the initial weight vector
W=[1 -1 0 .5]t . Inputs as X1= [1 -2 1.5 0] x2= [1 -0.5 -2 -1.5]; x3 = [0 1 -1 1.5] and C=1. Use
signum (bipolar binary activation function)
(10)
X1
X2
X3 X4 Net
F(net) W1 W2 W3 W4 Dw1 Dw2 Dw3 Dw4
1
-1
0
0.5
1
-2
1.5 0
3
1
2
-3
1.5 0.5 1
-2
1.5
0
-0.5
-2
-1
1.5 0.375
1
2.5
3.5
2
-1
0.5
2
1.5
1
-1
1.5 -3
1
3.5
4.5
0.5
0
-1
1
-1.5
1
-1
0
4. High speed rail monitoring devices sometimes make use of sensitive sensors to measure the
deflection of the earth when a rail car passes. These deflections are measured with respect
to some distance from the rail car and, hence are actually very small angles measured in
rnicroradians. Let a universe of deflection be A = [I, 2, 3, 4] where A is the angle in
microradians, and let a universe of distances be D = [), 2, 5, 7J where D is distance in feet,
suppose a relation between these two parameters has been determined as follows:
Now let a universe of rail car weights be W=[1,2], where W is the weight in units of 100,000
pounds. Suppose the fuzzy relation of W to A is given by
Using the two relations, find the relation RT0S = T
a. Using Max-min composition
1
0.4
0.5
1
0.3
0.3
0.2
0.1
b. Using Max-product composition
1
0.4
0.5
1
0.3
0.3
0.06
0.1
(5)
5. Consider a set P={p1, P2, P3, P4} of four varieties of paddy plants set D={D1,D2,D3,D4} of the
various diseases affecting the plants and S={S1 S2 S3 S4} be common symptoms of the
diseases. Let R be a relation on P*D and S be the relation on D*S. Find RoS given (5)
R= 0.6 0.6
0.9
0.8
S=
0.1
0.2
0.7
0.9
0.1 0.2
0.9
0.8
1
1
0.4
0.6
0.9 0.3
0.4
0.8
0
0
0.5
0.9
0.9 0.8
0.1
0.2
0.9
1
0.8
0.2
Obtain the association of the plants with the different symptoms of the diseases using
max-min composition
Grading scale
30 and above A
25 and above B
20 and above C
15 and above D
Else
E
0.8
0.8
0.8
0.9
0.8
0.8
0.8
0.9
0.8
0.8
0.8
0.9
0.8
0.8
0.4
0.9