An invariant variational principle for model-based interpolation of high dimensional clustered data

A self-consistent scheme based on the calculus of infinitesimal transformations, that describes model based interpolation of high dimensional data, constrained to lie on a nonlinear manifold is expressed as a dynamical system. The variational formulation derived for a single cluster is extended to the case of finite mixture models. The suggested formulation is shown to be qualitatively dissimilar properties, and exhibits greater computational efficiency, as compared with a scheme derived using “classical” variational calculus