# Persistent Homology in Sparse Regression and its Application to Brain Morphometry

arXiv: https://arxiv.org/abs/1409.0177 · HTML: https://mlsanity.com/paper/1409.0177/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2014.

## Built on by (most cited first, 3 of 3)

- [Quantum Distance Approximation for Persistence Diagrams](https://mlsanity.com/paper/2402.17295/) (2024)
- [Lattice Paths for Persistent Diagrams](https://mlsanity.com/paper/2105.00351/) (2021)
- [Cycles Communities from the Perspective of Dendrograms and Gradient Sampling](https://mlsanity.com/paper/2512.12974/) (2025)

## Abstract (arXiv)

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.