Page 159 - Introduction to Information Optics

144 2. Signal Processing with Optics

Training Set

Fig. 2.52. A block box representation of a Hopfield NN.

the ability to retrieve distorted and partial inputs. For example, a partial image
of A is presented to the Hopfield NN, as shown in Fig. 2.52. By repeated
iteration, we see that a recovered A is converged at the output end.

2.9.3. INTERPATTERN ASSOCIATION MODEL

Although the Hopfield neural network can retrieve erroneous or partial
patterns, the construction of the Hopfield neural network is through intrapat-
tern association, which ignores the association among the stored exemplars. In
other words, Hopfield would have a limited storage capacity and it is not
effective or even capable of retrieving similar patterns. One of the alternative
approaches is called interpattern association (IPA) neural network. An example
illustrating the IPA relationship is shown in Fig. 2.53, in which we assume that
Tony and George are identical twins. Nevertheless, we can identify them quite
easily by their special features: hair and mustache. Therefore, it is trivial by-
using a simple logic operation that an IPA neural network can be constructed.
For simplicity, let us consider a three-overlapping pattern as sketched in
Fig. 2.54, where the common and the special subspaces can be defined. If one
uses the following logic operations, an IPA neural network can be constructed:

/ = A A (B v C), // - B A (A v C), /// = C A (A v B)
IV = (A A B) A C, V = (B A C) A A, (2.138)

VI = (C A A) A B, VII = (A A B A C) A
where A , v , and ~ stand for AND, OR, and NOT logic operation, and 0
denotes the empty set.