TABLE OF CONTENTS In previous sections we described the emergence of orientation selectivity and of ocular dominance using PCA learning. It is interesting to examine whether it is possible to extract both under the same conditions. Cortical cells exhibit both orientation selectivity and varying degrees of ocular dominance, therefore it is essential that a successful model can develop both concurrently.
In this section we extend the exactly soluble model described above to the two eye case, this model is also exactly soluble. As before, true orientation selectivity does not emerge from this model because it is a 1D model, however the symmetry breaking which occurs can be thought of as an analog of orientation selectivity. In addition, as shown in Section 5.3.4, in higher dimensional cases all oriented solutions have zero DC. Thus, the simple 1-D case is comparable to the higher dimensional case, with the oscillating (zero-DC) solution representing the oriented solutions and the DC solution representing non-oriented solutions.
In the two eye case we can write down the general form of the two eye correlation function as
A simple example has the form Q ll = Q rr = Q and Q lr = Q rl = ?? Q thus
We use the same correlation function used in our soluble 1D model and assume that Q( x) = 1 + q cos( ? x).
Given that m(
