Tree Representations of Rectangular Proximity Matrices

Trends in Mathematical Psychology, R. Burggenhaut and V. Degreef (eds.), New York: North Holland, pp. 377-392

16 Pages Posted: 13 Jul 2017

See all articles by Wayne S. DeSarbo

Wayne S. DeSarbo

Pennsylvania State University

J. Carroll

Rutgers, The State University of New Jersey (Deceased)

Date Written: 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 least-squares fashion with closed-form formulas for estimating path length constants for de­riving path length trees.

Suggested Citation

DeSarbo, Wayne S. and Carroll, J., Tree Representations of Rectangular Proximity Matrices (1984). Trends in Mathematical Psychology, R. Burggenhaut and V. Degreef (eds.), New York: North Holland, pp. 377-392, Available at SSRN: https://ssrn.com/abstract=2783474

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

J. Carroll

Rutgers, The State University of New Jersey (Deceased)

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