Variable selection for cluster analysis is a difficult problem. The difficulty originates not only from the lack of class information but also the fact that high-dimensional data are often multifaceted and can be meaningfully clustered in multiple ways. In such a case the effort to find one subset of attributes that presumably gives the "best" clustering may be misguided. It makes more sense to facilitate variable selection by domain experts, that is, to systematically identify various facets of a data set (each being based on a subset of attributes), cluster the data along each one, and present the results to the domain experts for appraisal and selection. In this paper, we propose a generalization of the Gaussian mixture model, show its ability to cluster data along multiple facets, and demonstrate it is often more reasonable to facilitate variable selection than to perform it.
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