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...

Full description

Saved in:
Bibliographic Details
Published in:Multivariate behavioral research Vol. 27; no. 4; pp. 541 - 565
Main Authors: Krolak-Schwedt, Sabine, Eckes, Thomas
Format: Journal Article
Language:English
Published: Fort Worth, TX Lawrence Erlbaum Associates, Inc 01.10.1992
Society of Multivariate Experimental Psychology
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0027-3171
1532-7906
DOI:10.1207/s15327906mbr2704_3