# Sparse Hierachical Extrapolated Parametric Methods for Cortical Data Analysis

## TL;DR

This paper introduces a novel approach that leverages the hierarchical structure of icosahedral meshes in cortical data analysis, significantly accelerating data factorization methods like sparse dictionary learning.

## Contribution

It demonstrates how to exploit the hierarchical mesh structure for faster cortical data factorization and compares various methods on multiple neuroimaging datasets.

## Key findings

- Exploiting mesh hierarchy yields several orders of magnitude speedup.
- Different sparsity norms and extrapolation methods impact performance.
- The approach is validated on structural and functional MRI datasets.

## Abstract

Many neuroimaging studies focus on the cortex, in order to benefit from better signal to noise ratios and reduced computational burden. Cortical data are usually projected onto a reference mesh, where subsequent analyses are carried out. Several multiscale approaches have been proposed for analyzing these surface data, such as spherical harmonics and graph wavelets. As far as we know, however, the hierarchical structure of the template icosahedral meshes used by most neuroimaging software has never been exploited for cortical data factorization. In this paper, we demonstrate how the structure of the ubiquitous icosahedral meshes can be exploited by data factorization methods such as sparse dictionary learning, and we assess the optimization speed-up offered by extrapolation methods in this context. By testing different sparsity-inducing norms, extrapolation methods, and factorization schemes, we compare the performances of eleven methods for analyzing four datasets: two structural and two functional MRI datasets obtained by processing the data publicly available for the hundred unrelated subjects of the Human Connectome Project. Our results demonstrate that, depending on the level of details requested, a speedup of several orders of magnitudes can be obtained.