Support Vector Learning for Fuzzy Rule-Based Classification Systems
Yixin Chen and James Z. Wang
The Pennsylvania State University
Abstract:
To design a fuzzy rule-based classification system (fuzzy classifier)
with good generalization ability in a high dimensional feature space
has been an active research topic for a long time. As a powerful
machine learning approach for pattern recognition problems, support
vector machine (SVM) is known to have good generalization
ability. More importantly, an SVM can work very well on a high (or
even infinite) dimensional feature space. This paper investigates the
connection between fuzzy classifiers and kernel machines, establishes
a link between fuzzy rules and kernels, and proposes a learning
algorithm for fuzzy classifiers. We first show that a fuzzy classifier
implicitly defines a translation invariant kernel under the assumption
that all membership functions associated with the same input variable
are generated from location transformation of a reference function.
Fuzzy inference on the IF-part of a fuzzy rule can be viewed as
evaluating the kernel function. The kernel function is then proven to
be a Mercer kernel if the reference functions meet certain spectral
requirement. The corresponding fuzzy classifier is named positive
definite fuzzy classifier (PDFC). A PDFC can be built from the given
training samples based on a support vector learning approach with the
IF-part fuzzy rules given by the support vectors. Since the learning
process minimizes an upper bound on the expected risk (expected
prediction error) instead of the empirical risk (training error), the
resulting PDFC usually has good generalization. Moreover, because of
the sparsity properties of the SVMs, the number of fuzzy rules is
irrelevant to the dimension of input space. In this sense, we avoid
the ``curse of dimensionality.'' Finally, PDFCs with different
reference functions are constructed using the support vector learning
approach. The performance of the PDFCs is illustrated by extensive
experimental results. Comparisons with other methods are also
provided.
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Citation:
Yixin Chen and James Z. Wang, ``Support Vector Learning for Fuzzy
Rule-Based Classification Systems,'' IEEE Transactions on Fuzzy
Systems, vol. 11, no. 6, pp. 716-728, 2003.
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Last Modified:
January 10 2003
© 2003, Yixin Chen and James Z. Wang