  A general framework for dealing with both linear regression and clustering
problems is described. It includes Gaussian clusterwise linear regression
analysis with random covariates and cluster analysis via Gaussian mixture
models with variable selection. It also admits a novel approach for detecting
multiple clusterings from possibly correlated sub-vectors of variables, based
on a model defined as the product of conditionally independent Gaussian mixture
models. A necessary condition for the identifiability of such a model is
provided. The usefulness and effectiveness of the described methodology are
illustrated using simulated and real datasets.
