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On the Partitioning of Squared Euclidean Distance and its Applications in Cluster Analysis

Published online by Cambridge University Press:  01 January 2025

Randy L. Carter ,
Robin Morris  and
Roger K. Blashfield
Randy L. Carter*
Affiliation:
Department of Statistics, Division of Biostatistics J. Hillis Miller Health Center, University of Florida
Robin Morris
Affiliation:
Department of Psychology, Georgia State University
Roger K. Blashfield
Affiliation:
Department of Psychiatry, J. Hillis Miller Health Center, University of Florida
*
Requests for reprints should be sent to Randy L. Carter, Box J-212, J. Hillis Miller Health Center, Gainesville, FL 32610.
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Abstract

The partitioning of squared Eucliean distance between two vectors in M-dimensional space into the sum of squared lengths of vectors in mutually orthogonal subspaces is discussed and applications given to specific cluster analysis problems. Examples of how the partitioning idea can be used to help describe and interpret derived clusters, derive similarity measures for use in cluster analysis, and to design Monte Carlo studies with carefully specified types and magnitudes of differences between the underlying population mean vectors are presented. Most of the example applications presented in this paper involve the clustering of longitudinal data, but their use in cluster analysis need not be limited to this arena.

Keywords

squared Euclidean distanceorthogonal partitioningcluster analysisdescription of clustersderivation of similarity metricsdesign of Monte Carlo studieslongitudinal data
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 1 , March 1989 , pp. 9 - 23
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

The authors wish to thank Dr. Michael Resnick of the Department of Pediatrics at the University of Florida, Dr. Mario Ariet of the Department of Medicine, University of Florida and Children's Medical Services of the State of Florida for permission to use their child development data in our example. We also wish to express our appreciation to the referees and editors whose thorough reviews and detailed comments resulted in significant improvements to an earlier manuscript.

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