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5.13 Modular Neural Networks 233

The voting scheme in these ensemble networks can be implemented in a variety
of ways, the most common being the majority vote (choose the class label that
occurs more often at the module outputs), the max vote (choose the class label
corresponding to the maximum value of the activation function outputs) and the
average vote (choose the class label corresponding to the highest average value of
the activation function outputs of the modules). A detailed discussion about neural
network ensembles and voting schemes can be found in (Hansen and Salamon,
1990) and (Kittler et al., 1998), respectively.

'4'
I I I

.....

Vote
I

Figure 5.58. An ensemble network with k neural nets and a voting unit.

Table 5.10. Neural net solutions to the three-class cork stoppers problem.
Total
Network Features wl errors ~L)L errors @ errors
errors
MLP2:2:3 N, PRT 2 11 1 14
MLP2:2:3 N,ART 4 10 3 17
MLP3:3:3 N, PRM, ARTG 2 12 1 15
MLP3:3:3 N, PRTG, ARTG 14 4 2 20
MLP3:3:3 RAAR. ARTG, PRTG 6 8 2 16
Majority
(ensemble) 3 6 2 11
vote
Averaging (ensemble) 5 8 2 15

We illustrate this concept using the cork stoppers data example. Instead of using
the solution from section 5.6 (Table 5.3, we may choose to build an ensemble
network based on neural net solutions with a small number of weights, which were
found during the experimentation phase. All these nets were trained with great care
in order to achieve the best possible results, which are shown in Table 5.10. Notice
that the solutions have distinct qualities, with nets that recognize classes w, and y