Johnson has shown that the single linkage and complete linkage hierarchical clustering algorithms induce a metric on the data known as the ultrametric. Johnson's proof is extended to four other common clustering algorithms. Two additional methods also produce hierarchical structures which can violate the ultrametric inequality. (Author/CTM)

The classification capabilities of the one-dimensional Kohonen neural network (T. Kohonen, 1995) were compared with those of two partitioning and three hierarchical cluster methods in 2,580 data sets with known cluster structure. Overall, the performance of the Kohonen networks was similar to, or better than, that of the others. Implications for…

Using constraints with cluster analysis limits the possible number of clusters. This paper deals with clustering problems where grouping is constrained by a symmetric and reflexive relation. Two approaches, along with illustrations, are presented. (Author/JKS)

A general class of nonhierarchical clustering models and associated algorithms for fitting them are presented. These models generalize the Shepard-Arabie Additive clusters model. Two applications are given and extensions to three-way models, nonmetric analyses, and other model specifications are provided. (Author/JKS)

A nonspatial operationalization of the Krumhansl distance-density model of similarity is presented. The conceptual model and empirical evidence are reviewed. A nonspatial, tree-fitting methodology is described, which is sufficiently flexible to fit several competing hypotheses of similarity formation. Extensions to spatial models, three-way…

The present paper discusses two rather different types of partitioning techniques that still have the same property of monotone invariance. (Author)

The intent of this paper is to generalize the min and max clustering procedures in such a way that the assumption of a symmetric similarity measure is unnecessary. (Author)

A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)

A method is presented that simultaneously estimates cluster membership and corresponding regression functions for a sample of observations or subjects. This methodology is presented with the simulated annealing-based algorithm. A set of Monte Carlo analyses is included to demonstrate the performance of the algorithm. (SLD)

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)