Hierarchical Data Reduction and Learning
This work addresses data reduction challenges for applications like geospatial and numerical modeling, but appears incremental as it builds on existing hierarchical approximation methods.
The paper tackles the problem of generating sparse representations for multivariate datasets using a hierarchical learning strategy, achieving efficient data reconstruction and minimized prediction error across synthetic and real datasets.
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.