Cluster validity for fuzzy clustering algorithms

The proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm. It is assumed that the output of an algorithm includes a fuzzy nembership function for each data point. We show how to compute the proportion of possible m...

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Bibliographic Details
Published in:Fuzzy sets and systems 1981-01, Vol.5 (2), p.177-185
Main Author: Windham, Michael P.
Format: Article
Language:English
Subjects:
Cluster validity
Entropy
Fuzzy clustering algorithms
Fuzzy isodata algorithm
Partition coefficient
Proportion exponent
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Summary:The proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm. It is assumed that the output of an algorithm includes a fuzzy nembership function for each data point. We show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function, and use these proportions to define the proportion exponent. Its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals, namely, classification entropy and partition coefficient.
ISSN:0165-0114
1872-6801
DOI:10.1016/0165-0114(81)90015-4