# Hierarchical Data Reduction and Learning

## TL;DR

This paper introduces a hierarchical learning method for creating sparse data representations that effectively reduce data size while maintaining accuracy, with proven stability and convergence properties across various datasets.

## Contribution

It presents a novel hierarchical approach for data reduction that guarantees stability, convergence, and efficient data reconstruction, applicable to diverse datasets.

## Key findings

- Effective data reduction for synthetic and real datasets
- Accurate data reconstruction with minimized prediction error
- Stable and convergent approximation process

## Abstract

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.