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The Estimation of Ultrametric and Path Length Trees from Rectangular Proximity Data

Published online by Cambridge University Press:  01 January 2025

Geert De Soete ,
Wayne S. DeSarbo ,
George W. Furnas  and
J. Douglas Carroll
Geert De Soete*
Affiliation:
University of Ghent
Wayne S. DeSarbo*
Affiliation:
AT&T Bell Laboratories
George W. Furnas
Affiliation:
Bell Communications Research
J. Douglas Carroll
Affiliation:
AT&T Bell Laboratories
*
Requests for reprints should be sent either to G. De Soete, Department of Psychology, University of Ghent, Henri Dunantlaan 2, B-9000 Ghent, Belgium; or to W. S. DeSarbo, AT&T Bell Laboratories, Room 2C-256, 600 Mountain Avenue, Murray Hill, N.J. 07974.
Requests for reprints should be sent either to G. De Soete, Department of Psychology, University of Ghent, Henri Dunantlaan 2, B-9000 Ghent, Belgium; or to W. S. DeSarbo, AT&T Bell Laboratories, Room 2C-256, 600 Mountain Avenue, Murray Hill, N.J. 07974.
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Abstract

A least-squares algorithm for fitting ultrametric and path length or additive trees to two-way, two-mode proximity data is presented. The algorithm utilizes a penalty function to enforce the ultrametric inequality generalized for asymmetric, and generally rectangular (rather than square) proximity matrices in estimating an ultrametric tree. This stage is used in an alternating least-squares fashion with closed-form formulas for estimating path length constants for deriving path length trees. The algorithm is evaluated via two Monte Carlo studies. Examples of fitting ultrametric and path length trees are presented.

Keywords

Cluster AnalysisTrees
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 3 , September 1984 , pp. 289 - 310
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

G. De Soete is “Aspirant” of the Belgian “Nationaal Fonds voor Wetenschappelijk Onderzoek” at the University of Ghent, Belgium. W. S. DeSarbo and J. D. Carroll are Members of Technical Staff at AT&T Bell Laboratories, Murray Hill, N.J. G. W. Furnas is Member of Technical Staff at Bell Communications Research, Murray Hill, N.J.

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