Optimal variable weighting for hierarchical clustering: An alternating least-squares algorithm

This paper presents the development of a new methodology which simultaneously estimates in a least-squares fashion both an ultrametric tree and respective variable weightings for profile data that have been converted into (weighted) Euclidean distances. We first review the relevant classification literature on this topic. The new methodology is presented including the alternating least-squares algorithm used to estimate the parameters. The method is applied to a synthetic data set with known structure as a test of its operation. An application of this new methodology to ethnic group rating data is also discussed. Finally, extensions of the procedure to model additive, multiple, and three-way trees are mentioned.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek.