42.

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(3.49)

where n denotes the nth iteration, is the competition parameter introduced earlier (Figure 3.15b), and f(y) is generally a non-linear monotonically non-decreasing function, for example the sigmoid function, defined as:

(3.50)

The activities present in the F1 and F2 layers are also called short-term memory (STM), because they only exist when a signal (e.g. a training pattern) is passing through the layer.

After the identity of the winning neurone in layer F2 is determined, a process then starts to test system ‘vigilance’ according to:

(3.51)

where ρ ( [0, 1]) is a user-defined vigilance parameter.

If the test in Equation (3.51) fails, the current winning neurone is considered invalid and ruled out. The competitive process then starts again in F2 to search for an alternative winning neurone, which is again subject to the vigilance test. If the test in Equation (3.51) succeeds, only the weights, h_win,_j and g_j,win, linking to the winning neurone j and layer F1 are adjusted by the following rules:

(3.52)

where β ( [0, 1]) is the learning rate parameter. The concept of the ART1 clustering algorithm can be summarised in terms of three steps as shown in Figure 3.16.

3.5.2 Choice of parameters

The arrangement of weights h_ij in Equation (3.46), the choice of values for the vigilance parameter ρ, parameter α in Equation (3.35) and learning rate

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