Gennclus: New models for general nonhierarchical clustering analysis

A general class of nonhierarchical clustering models and associated algorithms for fitting them are presented. These (metric) clustering models generalize the Shepard-Arabie Additive Clusters model in allowing for: (1). either overlapping or nonoverlapping clusters; (2). either symmetric (one-way clustering) or nonsymmetric (two-way clustering) proximities (input data); and, (3). either symmetric or diagonal weights. The GENNCLUS algorithms utilize alternating least-squares methods combining ordinary and constrained least-squares, nonlinear constrained mathematical programming, and combinatorial optimization techniques in estimating model parameters. In addition to developing the mathematical bases of these models, a comprehensive set of Monte Carlo simulations of the different models is reported. Two applications concerning brand-switching data and celebrity-brand proximities are discussed. Finally, extensions to three-way models, nonmetric analyses, and other model specifications are provided.Wayne S. DeSarbo is a Member of Technical Staff in the Mathematics and Statistics Research Center at Bell Laboratories in Murray Hill, N.J. I wish to thank R. Gnanadesikan, J. D. Carroll, and P. Arabie for their comments on a previous draft of this paper. I also wish to acknowledge the computer assistance provided by Linda Clark. Finally, I wish to thank the reviewers and editor for their very complete reviews and comments.