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

PSYCHOMETRIKA--VOL. 49, NO. 3, 289-310

22 Pages Posted: 25 May 2016

See all articles by Geert De Soete

Geert De Soete

Ghent University

Wayne S. DeSarbo

Pennsylvania State University

George Furnas

Bell Communications Research

J. Carroll

Rutgers, The State University of New Jersey (Deceased)

Date Written: September 1984

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 leastsquares 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 Analysis, Trees

Suggested Citation

De Soete, Geert and DeSarbo, Wayne S. and Furnas, George and Carroll, J., The Estimation of Ultrametric and Path Length Trees from Rectangular Proximity Data (September 1984). PSYCHOMETRIKA--VOL. 49, NO. 3, 289-310, Available at SSRN: https://ssrn.com/abstract=2783445

Geert De Soete

Ghent University ( email )

Coupure Links 653
Gent, 9000
Belgium

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

George Furnas

Bell Communications Research

435 South Street
Morristown, NJ 07960-1961
United States

J. Carroll

Rutgers, The State University of New Jersey (Deceased)

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