43.

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Figure 3.16 Summary of ARTI clustering dynamics.

β in Equation (3.52) are issues that require more elaboration. As the weights h_ij are decreasing following their spatial index (as shown in Equation (3.46)), it follows that neurones with a low ordinal number (1, 2,…) are more likely to be selected than neurones with a high ordinal number. Thus, the set of winning neurones chosen by the system will follow a sequential order.

The vigilance parameter ρ in ART model controls the ‘tightness’ of a cluster. In the case of small values of the vigilance parameter ρ, Equation (3.51) allows more patterns to be associated with the same neurone in F2, and the result is a loose cluster. High value of the vigilance ρ will cause the network system to perform only exemplar learning (i.e. one pattern, one cluster) rather than category learning.

The value of the parameter α must be sufficiently large to affect the weights h and subsequently s in Equation (3.47). Normally, α is set to be greater than 0.001. The learning rate β controls how the system learns or adapts (Carpenter and Grossberg, 1987a, b). Learning rates that are too fast, in the extreme case, will make the system learn every input pattern as a new class, while learning rates that are too slow will make the system insensitive to new input patterns.

Fuzzy ARTMAP

Fuzzy ARTMAP is a supervised neural network that differs from ARTMAP in that fuzzy ARTMAP uses two fuzzy ART neural networks instead of two ART1 networks as its basic structure, and can therefore deal with either binary or analogue values. Before going on to consider the fuzzy ARTMAP network, it is necessary to introduce the basic properties of the fuzzy ART network.

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