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Learning Vector Quantization Networks
Architecture
The LVQ network architecture is shown below.
An LVQ network has a first competitive layer and a second linear layer. The competitive layer learns to classify input vectors in much the same way as the competitive layers of Self-Organizing and Learn. Vector Quant. Nets described in this chapter. The linear layer transforms the competitive layer's classes into target classifications defined by the user. We refer to the classes learned by the competitive layer as subclasses and the classes of the linear layer as target classes.
Both the competitive and linear layers have one neuron per (sub or target) class. Thus, the competitive layer can learn up to S1 subclasses. These, in turn, are combined by the linear layer to form S2 target classes. (S1 is always larger than S2.)
For example, suppose neurons 1, 2, and 3 in the competitive layer all learn subclasses of the input space that belongs to the linear layer target class No. 2. Then competitive neurons 1, 2, and 3, will have LW2,1 weights of 1.0 to neuron n2 in the linear layer, and weights of 0 to all other linear neurons. Thus, the linear neuron produces a 1 if any of the three competitive neurons (1,2, and 3) win the competition and output a 1. This is how the subclasses of the competitive layer are combined into target classes in the linear layer.
In short, a 1 in the ith row of a1 (the rest to the elements of a1 will be zero) effectively picks the ith column of LW2,1 as the network output. Each such column contains a single 1, corresponding to a specific class. Thus, subclass 1s from layer 1 get put into various classes, by the LW2,1a1 multiplication in layer 2.
We know ahead of time what fraction of the layer 1 neurons should be classified into the various class outputs of layer 2, so we can specify the elements of LW2,1 at the start. However, we have to go through a training procedure to get the first layer to produce the correct subclass output for each vector of the training set. We discuss this training shortly. First consider how to create the original network.
| | Examples | Creating an LVQ Network (newlvq) | |
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