Unsupervised learning: Exercise

1- Simulate the development of ocular dominance using a network with 2 input units (one right, one left) and one output unit. Use the following equation for the learning rule:

where N_u is the number of input units (2 in this case), n is a column vector of N_u 1’s, a is a learning rate (a =1 should work but try different values) and Q is equal to:

Do the weights lined up with the first or second eigenvector of Q? Do you get ocular dominance?

2- same as in 1 but with 101 output units and no lateral connections. Plot the weight pattern. Do you get ocular dominance? Do you get periodic columns? (Note: make sure that the normalization term is local to each output unit, i.e., its value should be specific to each unit on each iteration)

3- same as in 2 but this time, use the lateral connection kernel:

x is expressed in terms of number of units. The learning rule in this case is:

where K is the matrix whose rows are shifted copies of K(x) (make sure to treat x in K(x) as a periodic variable) and N is a 2x2 matrix of ones.

Do you get ocular dominance columns?

4- Verify that W and K have the same fundamental frequency.

5- Rerun the simulation with the following parameters:

What do you observe and why?

6- same as in 5 with: