41.

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Page 134

positive weight (generally a value of 1) is used, while negative connections (called the competition parameter, ) exist to every other neurone in F2, as illustrated in Figure 3.15b. The value is subject to the following constraint:

(3.44)

where m₂ is the total number of neurones in the F2 layer.

The learning strategy adopted by the ART model is that of the competitive learning, as described in Section 3.2. In the initial state, all of the weights g_ij are set to 1.0, as described by Carpenter and Grossberg (1987a), while the weights h_ij have to obey the restriction that h_ij must be greater than 0 and no bigger than (α+m₁)⁻¹, where a is a small positive constant and m₁ is the total number of neurones in layer F1. In general, for simplicity, the weights h_ij can all be set to:

(3.45)

However, an alternative is to let the h_ij decrease following their index order. Therefore, for example, the weights from the first neurone in F1 to all the neurones in F2, denoted by h_i1, i, will have the following relationship:

(3.46)

The effect of weight setting using either Equation (3.45) or Equation (3.46) is considered in Section 3.5.2.

During the learning process, a pattern vector X, X={x₁, x₂,…, x_n} is presented, and is converted to activity in the layer F1 and combined with linking weights h_ij to feed into the F2 layer in terms of:

(3.47)

where s_i is the input for neurone i in layer F2. An iterative process is then carried out to update the activity of each neurone in the F2 layer (so that neurones start to compete with each other) until finally only one winning neurone u_win is identified:

(3.48)

where u_i is the activity for the neurone i in F2, and is computed by

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