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We think of cluster analysis as class discovery. That is, we assume that there is an unknown mapping called clustering structure that assigns a class label to each observation, and the goal of cluster analysis is to estimate this clustering structure, that is, to estimate the number of clusters and cluster assignments. In traditional cluster analysis, it is assumed that such unknown mapping is unique. However, since the observations may cluster in more than one way depending on the variables used, it is natural to permit the existence of more than one clustering structure. This generalized clustering problem of estimating multiple clustering structures is the focus of this paper. We propose an algorithm for finding multiple clustering structures of observations which involves clustering both variables and observations. The number of clustering structures is determined by the number of variable clusters. The dissimilarity measure for clustering variables is based on nearest-neighbor graphs. The observations are clustered using weighted distances with weights determined by the clusters of the variables.  The motivating application is to gene expression data.

A Generalized Clustering Problem, with Application to DNA Microarrays