1. [10 points] Consider a neural network with two inputs and three neurons in the competitive layer. The input vectors in the training set have the values
x
= −1 , x
2
1
0
= 0 , x
3
1
=
1/
1/
2
2
,
and the initial weight vectors are
w = 0
, w =
− 2 /
5
, w
1
2
3
−1
5
1/
a) Plot the input vectors and initial weights on a unit circle.
=
−1/
5
2 /
5
.
b) Calculate the resulting weights found after training the neurons with competitive learning rule using
learning rate =0.5, on the following sequence of inputs:
x
, x
2
, x
, x
, x
2
, x .
Note: Weights must always
1
3
1
3
lie on a unit circle, and thus must be re-normalized after each iteration.
c) Analyze the resulting weights and elaborate on the final weight distribution with respect to the input vectors.
