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Assignment 7 Solution

[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.

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