Dimensionality reduction approach to multivariate prediction

Dimensionality reduction methods used for prediction can be cast into a general framework by deriving them from a common objective function. Such a function yields continuum of different solutions, including all the known ones. Least-squares and maximum likelihood estimation of the model at the base of dimensionality reduction methods for prediction lead to an additive objective function. By letting this additive function be any convex linear combination of the two addends, another objective function from which a continuum of solutions can be obtained.