  This paper describes a hierarchical learning strategy for generating sparse
representations of multivariate datasets. The hierarchy arises from
approximation spaces considered at successively finer scales. A detailed
analysis of stability, convergence and behavior of error functionals associated
with the approximations are presented, along with a well chosen set of
applications. Results show the performance of the approach as a data reduction
mechanism for both synthetic (univariate and multivariate) and real datasets
(geospatial and numerical model outcomes). The sparse representation generated
is shown to efficiently reconstruct data and minimize error in prediction.
