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We propose a hierarchical learning strategy aimed at generating sparserepresentations and associated models for large noisy datasets. The hierarchyfollows from approximation spaces identified at successively finer scales. Forpromoting model generalization at each scale, we also introduce a novel,projection based penalty operator across multiple dimension, using permutationoperators for incorporating proximity and ordering information. The paperpresents a detailed analysis of approximation properties in the reconstructionReproducing Kernel Hilbert Spaces (RKHS) with emphasis on optimality andconsistency of predictions and behavior of error functionals associated withthe produced sparse representations. Results show the performance of theapproach as a data reduction and modeling strategy on both synthetic(univariate and multivariate) and real datasets (time series). The sparse modelfor the test datasets, generated by the presented approach, is also shown toefficiently reconstruct the underlying process and preserve generalizability.

Hierarchical regularization networks for sparsification based learning on noisy datasets