  Finite mixtures of regression models offer a flexible framework for
investigating heterogeneity in data with functional dependencies. These models
can be conveniently used for unsupervised learning on data with clear
regression relationships. We extend such models by imposing an
eigen-decomposition on the multivariate error covariance matrix. By
constraining parts of this decomposition, we obtain families of parsimonious
mixtures of regressions and mixtures of regressions with concomitant variables.
These families of models account for correlations between multiple responses.
An expectation-maximization algorithm is presented for parameter estimation and
performance is illustrated on simulated and real data.
