Pattern Recognition with Fuzzy Objective Function AlgorithmsThe fuzzy set was conceived as a result of an attempt to come to grips with the problem of pattern recognition in the context of imprecisely defined categories. In such cases, the belonging of an object to a class is a matter of degree, as is the question of whether or not a group of objects form a cluster. A pioneering application of the theory of fuzzy sets to cluster analysis was made in 1969 by Ruspini. It was not until 1973, however, when the appearance of the work by Dunn and Bezdek on the Fuzzy ISODATA (or fuzzy c-means) algorithms became a landmark in the theory of cluster analysis, that the relevance of the theory of fuzzy sets to cluster analysis and pattern recognition became clearly established. Since then, the theory of fuzzy clustering has developed rapidly and fruitfully, with the author of the present monograph contributing a major share of what we know today. In their seminal work, Bezdek and Dunn have introduced the basic idea of determining the fuzzy clusters by minimizing an appropriately defined functional, and have derived iterative algorithms for computing the membership functions for the clusters in question. The important issue of convergence of such algorithms has become much better understood as a result of recent work which is described in the monograph. |
Contents
Partitions and Relations | 15 |
Objective Function Clustering | 43 |
Cluster Validity | 95 |
Copyright | |
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Other editions - View all
Pattern Recognition with Fuzzy Objective Function Algorithms James C. Bezdek No preview available - 2012 |
Pattern Recognition with Fuzzy Objective Function Algorithms James C Bezdek No preview available - 1981 |
Common terms and phrases
algorithms Analysis applied Bayesian classifier c-means algorithms Calculate centroid classifier design cluster centers cluster validity clustering algorithms clustering criterion coefficient column conv(B convergence convex combination convex hull covariance matrix CWS clusters D₁ data points data set decision regions defined Definition denote distance empirical error rate entropy equations estimates Euclidean norm example finite fixed fuzzy c-means fuzzy c-partition fuzzy clustering fuzzy set fuzzy subsets geometric hard c-partition hard clusters hyperplane iterations Jvrm k-NN labeled linear varieties local minima mathematical matrix maximum measure membership function method Mfco minimize minimum models objective function observations optimal p₁ pair parameters partition pattern recognition Picard iteration probability proof prototypes Ruspini sample solutions statistical structure substructure Table Theorem u₁ unique UPGMA v₁ values vectors zero Σ Σ