C++ Neural Networks and Fuzzy Logic: Preface

Learning Vector Quantizer

Suppose the goal is the classification of input vectors. Kohonen’s Vector Quantization is a method in which

you first gather a finite number of vectors of the dimension of your input vector. Kohonen calls these

codebook vectors. You then assign groups of these codebook vectors to the different classes under the

classification you want to achieve. In other words, you make a correspondence between the codebook vectors

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and classes, or, partition the set of codebook vectors by classes in your classification.

Now examine each input vector for its distance from each codebook vector, and find the nearest or closest

codebook vector to it. You identify the input vector with the class to which the codebook vector belongs.

Codebook vectors are updated during training, according to some algorithm. Such an algorithm strives to

achieve two things: (1), a codebook vector closest to the input vector is brought even closer to it; and (two), a

codebook vector indicating a different class is made more distant from the input vector.

For example, suppose (2, 6) is an input vector, and (3, 10) and (4, 9) are a pair of codebook vectors assigned

to different classes. You identify (2, 6) with the class to which (4, 9) belongs, since (4, 9) with a distance of

[radic]13 is closer to it than (3, 10) whose distance from (2, 6) is [radic]17. If you add 1 to each component of

(3, 10) and subtract 1 from each component of (4, 9), the new distances of these from (2, 6) are [radic]29 and

[radic]5, respectively. This shows that (3, 10) when changed to (4, 11) becomes more distant from your input

vector than before the change, and (4, 9) is changed to (3, 8), which is a bit closer to (2, 6) than (4, 9) is.

Training continues until all input vectors are classified. You obtain a stage where the classification for each

input vector remains the same as in the previous cycle of training. This is a process of self−organization.

The Learning Vector Quantizer (LVQ) of Kohonen is a self−organizing network. It classifies input vectors on

the basis of a set of stored or reference vectors. The B field neurons are also called grandmother cells, each of

which represents a specific class in the reference vector set. Either supervised or unsupervised learning can be

used with this network. (See Figure 6.2.)

Figure 6.2

  Layout for Learning Vector Quantizer.

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Unsupervised Networks

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