Page 430 - Introduction to Information Optics

7.8. Neural Pattern Recognition 41
data are provided, while the desired output result is not. After a single trial or
series of trials, an evaluation rule (previously provided to the NN) is used to
evaluate the performance of the network. Thus, we see that the network is
capable of adapting and categorizing the unknown objects. This kind of
self-organizing process is, in fact, a representation of the self-learning capability
of a human brain.
To simplify our discussion, we will discuss here only the Kohonen's
self-organizing feature map. Kohonen's model is the best-known unsupervised
learning model; it is capable of performing statistical pattern recognition and
classification, and it can be modified for optical implementation.
Knowledge representation in human brains is generally at different levels of
abstraction and assumes the form of a feature map. Kohonen's model suggests
a simple learning rule by continuously adjusting the interconnection weights
between input and output neurons based on the matching score between the
input and the memory matrix. A single-layer NN consists of N x N input and
M x M output neurons, as shown in Fig. 7.50. Assume that a set of 2-D vectors
(i.e., input patterns) are sequentially presented to the NN, as given by

(7.71;

where t represents the time index and (i,./) specifies the position of the input
neuron. Thus, the output vectors of the NN can be expressed as the weighted

Output space: MxM output neurons

Input space: NxN input neurons

Fig. 7.50. A single-layer Kohonen NN.