Page 431 - Introduction to Information Optics

7. Pattern Recognition with Optics

Memory space:

Fig. 7.51. Memory vectors in the memory matrix space.

sum of the input vectors,
N N
m mj(t)x y (f ), = 1 , 2, . . . , M, (7.72)

where y lk(t) represents the state of the (/, fe)th neuron in the output space and
m lkij(t) is the interconnection weight between the (i, ;)th input and the (/, fc)th
output neurons. The preceding equation can also be written in matrix form, as
given by

y lk(t) = m lk(t)\(t),

where m lk(t) can be expanded in an array of 2-D submatrices, as shown in Fig.
7.51, Each submatrix can be written in the form

m •IklN
m lk2l(t) m lk2N
(7.73)

m (fcJVl (0 m lkNN\
where the elements in each submatrix represent the associative weight factors
from each of the input neurons to one output neuron.
Notice that the Kohenen model does not, in general, specify the desired
output results. Instead, a matching criterion is defined to find the best match
between the input vector and the memory vectors and then determine the best