Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration

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Chapter 7 Fuzzy Clustering

7.7 Fuzzy Adaptive Clustering

Many of the behavioral problems with the standard fuzzy c-means algo-

rithm are eliminated when we relax the probabilistic constraint imposed

by Expression 7.10. Such an approach has been developed by Krishnapu-

ram and Keller (see “Further Reading”) and later expanded by Young-Jun

Lee (see “Further Reading”) in his doctoral thesis. In fuzzy adaptive

clustering, the constraint on data point memberships is imposed by

Expression 7.17.

p



j=1

n



i=1

μ

j

(x

i

) = n (7.17)

Here,

μ

j

(x

i

) is the membership of x

i

in the j-th cluster

p is the number of specified clusters

n is the number of data points

With this more relaxed restriction in hand, the total membership quan-

tifiers for all sample points equal n (the