A Graph Theoretic Criterion for Determining the Number of Clusters in a Data Set

This article is concerned with procedures for determining the number of clusters in a data set. Most of the procedures or stopping rules currently in use involve finding internally coherent and externally isolated clusters, but do not derive from the formal structure of the respective clustering mod...

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Vydané v:Multivariate behavioral research Ročník 27; číslo 4; s. 541 - 565
Hlavní autori: Krolak-Schwedt, Sabine, Eckes, Thomas
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Fort Worth, TX Lawrence Erlbaum Associates, Inc 01.10.1992
Society of Multivariate Experimental Psychology
Predmet:
Biological and medical sciences
Cluster Analysis
Data Collection
Equations (Mathematics)
Evaluation Criteria
Fundamental and applied biological sciences. Psychology
Graph Theory
Hierarchical Cluster Analysis
Mathematical Models
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics. Statistics. Methodology
Statistics. Mathematics
Stopping Rules
Cluster analysis
Statistical method
Selection criterion
Stopping rule
Graph theory
ISSN:0027-3171, 1532-7906
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Abstract This article is concerned with procedures for determining the number of clusters in a data set. Most of the procedures or stopping rules currently in use involve finding internally coherent and externally isolated clusters, but do not derive from the formal structure of the respective clustering model. Based on the graph theoretic concepts of minimal spanning tree, maximal spanning tree, and homomorphic function, a new criterion is advanced that yields a well-defined clustering solution. Its performance in determining the number of clusters in several empirical data sets is evaluated by comparing it to four prominent stopping rules. It is shown that the proposed criterion not only possesses mathematically attractive properties but also may contribute to solving the number-of-clusters problem.
AbstractList This article is concerned with procedures for determining the number of clusters in a data set. Most of the procedures or stopping rules currently in use involve finding internally coherent and externally isolated clusters, but do not derive from the formal structure of the respective clustering model. Based on the graph theoretic concepts of minimal spanning tree, maximal spanning tree, and homomorphic function, a new criterion is advanced that yields a well-defined clustering solution. Its performance in determining the number of clusters in several empirical data sets is evaluated by comparing it to four prominent stopping rules. It is shown that the proposed criterion not only possesses mathematically attractive properties but also may contribute to solving the number-of-clusters problem.
Procedures for determining the number of clusters in a data set are explored. A proposed stopping rule, the GRAPH criterion, is compared to four stopping rules currently in use. The GRAPH criterion's mathematically attractive properties and utility in solving the number-of-clusters problem are demonstrated. (SLD)
Author Eckes, Thomas
Krolak-Schwedt, Sabine
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10.1007/BF02294065
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Keywords Cluster analysis
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Selection criterion
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Graph theory
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Society of Multivariate Experimental Psychology
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Snippet This article is concerned with procedures for determining the number of clusters in a data set. Most of the procedures or stopping rules currently in use...
Procedures for determining the number of clusters in a data set are explored. A proposed stopping rule, the GRAPH criterion, is compared to four stopping rules...
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SubjectTerms Biological and medical sciences
Cluster Analysis
Data Collection
Equations (Mathematics)
Evaluation Criteria
Fundamental and applied biological sciences. Psychology
Graph Theory
Hierarchical Cluster Analysis
Mathematical Models
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics. Statistics. Methodology
Statistics. Mathematics
Stopping Rules
Title A Graph Theoretic Criterion for Determining the Number of Clusters in a Data Set
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