Databases Reference
In-Depth Information
Here we follow a fuzzy classifier design method based on cluster
estimation.
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The main characteristics of this approach are:
(1) An initial fuzzy classification model is derived by cluster estimation.
(2) The fuzzy rule base contains a separate set of fuzzy rules for each class.
(3) Double-sided Gaussian membership
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functions are employed for the
premise parts of the fuzzy rules. These are more flexible than the typical
Gaussian kernel.
(4) The classification outcome is determined by the rule with the highest
activation.
(5) Training is performed by a hybrid learning algorithm, which combines
gradient-based and heuristic adaptation of the membership functions
parameters. Only the rules with the maximum activation per class are
updated for each pattern. The cost function to be minimized is a
measure of the degree to which the rules for each class are activated
when a pattern that belongs to that particular class is inserted.
Specifically, for each pattern, the cost is defined as:
1
2
(1
µ
c,max
+
µ
¬
c,max
)
2
E
=
−
(8.9)
where
µ
c,max
is the firing strength of the rule among the set of rules
belonging to the correct class, which achieves the maximum activation
among the correct class rules, while
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is the firing strength of the fuzzy
rule, which belongs to the wrong class and achieves the maximum
activation amongst the rules of its class. In such fuzzy models, it is
straightforward to study the effect of removing an input, by simply
removing all the antecedent clauses which are associated with the
deleted input.
8.5. Multi-Objective Genetic Algorithm for Feature Selection
Feature selection can naturally be posed as a multi-objective search
problem, since in the simplest case it involves minimization of both
the subset cardinality and modeling error. Therefore, multi-objective
evolutionary algorithms (MOEA) are well suited for feature selection.
Evolutionary Multi-Objective Feature Selection (EMOFS)
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is employed
to handle such objectives, namely the specificity and sensitivity of
classifiers (shown in Fig. 8.8). The obvious choice for assessing a classifier's
performance is to estimate its misclassification rate. Yet, in many problem
domains, such as in engineering or medical diagnosis, it makes more
