## Abstract

Nonsupervised pattern recognition is addressed and the concept of fuzzy sets is explored in order to provide the investigator (data analyst) additional information supplied by the pattern class membership values apart from the classical pattern class assignments. The basic ideas behind the pattern recognition problem, the clustering problem, and the concept of fuzzy sets in cluster analysis are discussed, and a brief review of the literature of the fuzzy cluster analysis is given. Some mathematical aspects of fuzzy set theory are briefly discussed; in particular, a measure of fuzziness is suggested. The optimization-clustering problem is characterized. Then the fundamental idea behind affinity decomposition is considered. Next, further analysis takes place with respect to the partitioning-characterization functions. The iterative optimization procedure is then addressed. The reclassification function is investigated and convergence properties are examined. Finally, several experiments in support of the method suggested are described. Four object data sets serve as appropriate test cases. 120 references, 70 figures, 11 tables. (RWR)

## Citation Formats

Backer, E.
Cluster analysis by optimal decomposition of induced fuzzy sets.
Netherlands: N. p.,
1978.
Web.

Backer, E.
Cluster analysis by optimal decomposition of induced fuzzy sets.
Netherlands.

Backer, E.
1978.
"Cluster analysis by optimal decomposition of induced fuzzy sets."
Netherlands.

@misc{etde_7182529,

title = {Cluster analysis by optimal decomposition of induced fuzzy sets}

author = {Backer, E}

abstractNote = {Nonsupervised pattern recognition is addressed and the concept of fuzzy sets is explored in order to provide the investigator (data analyst) additional information supplied by the pattern class membership values apart from the classical pattern class assignments. The basic ideas behind the pattern recognition problem, the clustering problem, and the concept of fuzzy sets in cluster analysis are discussed, and a brief review of the literature of the fuzzy cluster analysis is given. Some mathematical aspects of fuzzy set theory are briefly discussed; in particular, a measure of fuzziness is suggested. The optimization-clustering problem is characterized. Then the fundamental idea behind affinity decomposition is considered. Next, further analysis takes place with respect to the partitioning-characterization functions. The iterative optimization procedure is then addressed. The reclassification function is investigated and convergence properties are examined. Finally, several experiments in support of the method suggested are described. Four object data sets serve as appropriate test cases. 120 references, 70 figures, 11 tables. (RWR)}

place = {Netherlands}

year = {1978}

month = {Jan}

}

title = {Cluster analysis by optimal decomposition of induced fuzzy sets}

author = {Backer, E}

abstractNote = {Nonsupervised pattern recognition is addressed and the concept of fuzzy sets is explored in order to provide the investigator (data analyst) additional information supplied by the pattern class membership values apart from the classical pattern class assignments. The basic ideas behind the pattern recognition problem, the clustering problem, and the concept of fuzzy sets in cluster analysis are discussed, and a brief review of the literature of the fuzzy cluster analysis is given. Some mathematical aspects of fuzzy set theory are briefly discussed; in particular, a measure of fuzziness is suggested. The optimization-clustering problem is characterized. Then the fundamental idea behind affinity decomposition is considered. Next, further analysis takes place with respect to the partitioning-characterization functions. The iterative optimization procedure is then addressed. The reclassification function is investigated and convergence properties are examined. Finally, several experiments in support of the method suggested are described. Four object data sets serve as appropriate test cases. 120 references, 70 figures, 11 tables. (RWR)}

place = {Netherlands}

year = {1978}

month = {Jan}

}