Computational Intelligence Techniques - Computational Intelligence in Biomedical Engineering - page 124

Now the larger the learning rate λ , the faster the learning at the expense
of overshooting the optimal E s MLP . To account for this, it is possible to add
metarules to the optimization step, an example meta rule being

if ∆ E s MLP changes then λ changes

This augmentation is also known as meta learning and has shown improved
performance compared to the standard update rules found in classical
optimization.
Fuzzy perceptrons have also been introduced by Keller and Hunt (1985) to
perform data clustering and automatically determine the prototype clusters
and class memberships of individual patterns. The update of the perceptron
weights is modified to

w t +1
j

= w j + cx j

p

u 1 j − u 2 j

where u ij is the membership grade of the i th training pattern whereas c and p
are predetermined scalars, which respectively affect the learning rate and the
norm in which the computation takes place.
A general fuzzy neural system (Figure 3.26) usually has inputs consisting
of rules where the conditions and consequents are selected a priori. Numeric
rules such as

if x =1 . 2 then y =4 . 5

tend to be overly specific and brittle in the sense that they are activated only
when the exact condition is met. Alternatively, fuzzy relations are applied over
the Cartesian product of input variables such as A 1 , A 2 ,..., A m and output
space variables B 1 , B 2 ,..., B n to soften the conditions. The objective now is
to discover meaningful rules between the inputs and outputs, that is, A i and
B j . In this system the strength of the relationship between the fuzzy input
and output variables can be depicted by an association matrix. The input
conditions form the m columns of the matrix and the output consequents
form the n rows. Each row indicates what the required conclusions are for the
given conditions, so if only one dominant element is in the row, then only a
single rule is available. If no dominant element exists, the particular rule is
insignificant. Besides that, it is also possible to have k dominant elements in

A 1

B 1

A 2

B 2

Neural network

B n

A m

FIGURE 3.26
A basic neural network with fuzzified inputs and outputs. The inputs represent
linguistic variables or rules.