Additive two-mode clustering: The error-variance approach revisited

The additive clustering approach is applied to the problem of two-mode clustering and compared with the recent error-variance approach of Eckes and Orlik (1993). Although the schemes of the computational algorithms look very similar in both of the approaches, the additive clustering has been shown to have several advantages. Specifically, two technical limitations of the error-variance approach (see Eckes and Orlik 1993, p. 71) have been overcome in the framework of the additive clustering. The research was supported by the Office of Naval Research under grant number N0014-93-1-0222 to Rutgers University. The authors are indebted both to Fionn Murtagh, who served as Acting Editor, and to anonymous Referees for thoughtful and constructive reviews.     

A new approach to isotonic agglomerative hierarchical clustering

Hierarchical clustering methods must be isotonic for the construction of ultrametric. We present a general strategy to widen the class of isotonic methods implemented by agglomerative algorithms. At each step of the agglomeration we allow one of several admissible pairs to be chosen. Then under mild assumptions an appropriate definition of admissibility guarantees isotony. Moreover we consider the use of the new methods to compute locally optimal ultrametrics. Two examples demonstrate the ability to define new agglomerative methods superior to their traditional competitors.     

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.     

Partial dissimilarities with application to clustering

We consider dissimilarities which are defined only on some pairs of items. Such situations may occur in some problems like unfolding or merging, or can be encountered as an intermediate step of a more general transformation. We give necessary and sufficient conditions for the existence of extensions with good properties and characterize the family of such extensions. Using partial dissimilarities we construct a dissimilarity-into-distance transformation family.The author thanks the editor and two anonymous referees for their suggestions and their helpful comments.