# Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest

arXiv: https://arxiv.org/abs/2201.00087 · HTML: https://mlsanity.com/paper/2201.00087/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 116 references that are in the map.
- First posted on arXiv 1 Jan 2022.

## Builds on (most cited first, 18 of 18)

- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [EEG-GAN: Generative adversarial networks for electroencephalograhic (EEG) brain signals](https://mlsanity.com/paper/1806.01875/) (2018)
- [Connectivity-Optimized Representation Learning via Persistent Homology](https://mlsanity.com/paper/1906.09003/) (2019)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data](https://mlsanity.com/paper/1601.01704/) (2016)
- [Fr'echet Means and Procrustes Analysis in Wasserstein Space](https://mlsanity.com/paper/1701.06876/) (2017)
- [Manifold-regression to predict from MEG/EEG brain signals without source modeling](https://mlsanity.com/paper/1906.02687/) (2019)
- [Cliques and Cavities in the Human Connectome](https://mlsanity.com/paper/1608.03520/) (2016)
- [The importance of the whole: topological data analysis for the network neuroscientist](https://mlsanity.com/paper/1806.05167/) (2018)
- [Variational Wasserstein Clustering](https://mlsanity.com/paper/1806.09045/) (2018)
- [A Graph Gaussian Embedding Method for Predicting Alzheimer's Disease Progression with MEG Brain Networks](https://mlsanity.com/paper/2005.05784/) (2020)
- [Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer](https://mlsanity.com/paper/1809.06433/) (2018)
- [Topological Learning for Brain Networks](https://mlsanity.com/paper/2012.00675/) (2020)
- [Statistical Model for Dynamically-Changing Correlation Matrices with Application to Brain Connectivity](https://mlsanity.com/paper/1812.10050/) (2018)
- [Smile-GANs: Semi-supervised clustering via GANs for dissecting brain disease heterogeneity from medical images](https://mlsanity.com/paper/2006.15255/) (2020)
- [A Robust and Unified Framework for Estimating Heritability in Twin Studies using Generalized Estimating Equations](https://mlsanity.com/paper/1710.09326/) (2017)

## Built on by (most cited first, 1 of 1)

- [Data-driven techniques for translational neuroscience and personalized neuro-health](https://mlsanity.com/paper/2608.13749/) (2026)

## Abstract (arXiv)

We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure topological differences, enabling the clustering of brain networks into distinct topological states. This technique outperforms the commonly used k-means clustering in identifying brain network state spaces by effectively incorporating the temporal dynamics of the data without the need for explicit model specification. We further investigate the genetic underpinnings of these topological features using a twin study design, examining the heritability of such state changes. Our findings suggest that the topology of brain networks, particularly in their dynamic state changes, may hold significant hidden genetic information. MATLAB code for the method is available at https://github.com/laplcebeltrami/PH-STAT.