22.

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where j′ denotes the neighbourhood of j including j itself. The term γⁿ is also a time-decaying function, and is defined by:

(3.15)

Usually, a value of γ_min in the region of 1.0 is chosen, and γ_max can be set sufficiently large to make the neighbourhood function β_j′ (γⁿ) cover the whole output layer.

Equation (3.14) indicates that, for j′ = j, i.e. for the winning neurone itself, the updating magnitude for the associated weights is proportional to the learning rate α (because β_j′=β_j=1). The updating magnitude for other j′ (i.e. the magnitude of change in j′) is sequentially decreasing with the increasing distance between the neighbourhood j′ and the winning neurone j. Figure 3.7 illustrates the update in neighbourhood function as a time-decreasing function.

Different values of the functions γ and α produce different effects on the

Figure 3.7 Modification of the weights of those neurones around a selected neurone begins with a wide neighbourhood that decreases in size following training time n2> n1>n0.

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