46.

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Page 139

nated by the subscripts or superscripts a and b. Figure 3.18b illustrates the linkages between Fab and both F2a (in the case of three neurones) and F2b (in the case of two desired categories). The structure of the F2a and F2b layers is the same as shown in Figure 3.15b. However, for simplicity, both self-linkage and inter-neurone linkages are ignored. Each neurone in F2a is linked to all Fab neurones by ways of wkia, while neurones in F2b are connected to Fab in terms of one-to-one pathways in both directions (F2b → Fab and F2b → Fab). The variables ukb and zkab each denotes the output of F2b and Fab, respectively. The inputs for both ARTa and ARTb are normalised in terms of complement coding. An input vector X, becomes , where , for i =1 to n, while the rest of the elements remain the same. Complement coding provides a useful means of solving a potential fuzzy ART category proliferation problem (Carpenter et al., 1991a).

During training, the initialisation process for weights within the ARTa and ARTb is the same as described in Section 3.5.1. The weights (F2a →Fab) are initialised to the value of unity. Once a training pair (i.e. data features and desired category) is presented to the fuzzy ARTMAP, ARTa and ARTb are triggered to determine their own winning neurones on F2a and F2b using the procedures described in Figure 3.16, steps (1) and (2). Let I denote the winning neurone in F2a. The variable in Fab is then computed by

(3.54)

and subjected to the vigilance test:

(3.55)

where ρab is the vigilance parameter for Fab. The purpose of Equation (3.55) is in fact to test if ARTa favours the same category as shown in ARTb. If the test in Equation (3.55) does not succeed, the vigilance in ARTa, denoted by ρa, is increased by an amount which is sufficiently large so as to make the current ARTa winner neurone invalid, i.e.

(3.56)

The variables in Equation (3.56) are the same as those defined in Section

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Classification Methods for Remotely Sensed Data
Classification Methods for Remotely Sensed Data, Second Edition
ISBN: 1420090720
EAN: 2147483647
Year: 2001
Pages: 354

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