Optimality tests for fixed points of the fuzzy c-means algorithm

DOI10.1016/0031-3203(88)90037-4zbMath0662.68099OpenAlexW2036571822MaRDI QIDQ1114435

Taehwan Kim, James C. Bezdek, Richard J. Hathaway

Publication date: 1988

Published in: Pattern Recognition (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0031-3203(88)90037-4

zbMATH Keywords

constrained optimizationcluster analysisconvergence theorygradient projection methodKuhn-Tucker conditionsfuzzy c- meansZangwill's theory

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Pattern recognition, speech recognition (68T10)

Related Items

A fuzzy clustering algorithm for graph bisection, Optimality tests for the fuzzy \(c\)-means algorithm, Global optimization in clustering using hyperbolic cross points, On the mathematical and numerical properties of the fuzzy \(c\)-means algorithm, Coresets for Fuzzy K-Means with Applications, A survey of fuzzy clustering

Cites Work

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• Local convergence of the fuzzy c-means algorithms
• Fuzzy c-means: optimality of solutions and effective termination of the algorithm
• Numerical taxonomy with fuzzy sets
• An approach to nonlinear programming
• On the Local Optimality of the Fuzzy Isodata Clustering Algorithm
• Convergence theory for fuzzy c-means: Counterexamples and repairs
• A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms
• Detection and Characterization of Cluster Substructure II. Fuzzy c-Varieties and Convex Combinations Thereof
• A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters
• Cluster Validity with Fuzzy Sets