# Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence

arXiv: https://arxiv.org/abs/2006.07882 · HTML: https://mlsanity.com/paper/2006.07882/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2020.

## Built on by (most cited first, 26 of 26)

- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Exploring the Geometry and Topology of Neural Network Loss Landscapes](https://mlsanity.com/paper/2102.00485/) (2021)
- [Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction](https://mlsanity.com/paper/2203.01703/) (2022)
- [Euler Characteristic Tools For Topological Data Analysis](https://mlsanity.com/paper/2303.14040/) (2023)
- [Topology-Aware Focal Loss for 3D Image Segmentation](https://mlsanity.com/paper/2304.12223/) (2023)
- [Topological Signatures vs. Gradient Histograms: A Comparative Study for Medical Image Classification](https://mlsanity.com/paper/2507.03006/) (2025)
- [HOG-CNN: Integrating Histogram of Oriented Gradients with Convolutional Neural Networks for Retinal Image Classification](https://mlsanity.com/paper/2507.22274/) (2025)
- [Learning shared neural manifolds from multi-subject FMRI data](https://mlsanity.com/paper/2201.00622/) (2021)
- [Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices](https://mlsanity.com/paper/2303.05286/) (2023)
- [The magnitude vector of images](https://mlsanity.com/paper/2110.15188/) (2021)
- [Deep Regression Representation Learning with Topology](https://mlsanity.com/paper/2404.13904/) (2024)
- [BLIS-Net: Classifying and Analyzing Signals on Graphs](https://mlsanity.com/paper/2310.17579/) (2023)
- [Persistent Homology-induced Graph Ensembles for Time Series Regressions](https://mlsanity.com/paper/2503.14240/) (2025)
- [When Witnesses Defend: A Witness Graph Topological Layer for Adversarial Graph Learning](https://mlsanity.com/paper/2409.14161/) (2024)
- [Differentially Private Topological Data Analysis](https://mlsanity.com/paper/2305.03609/) (2023)
- [Discrete transforms of quantized persistence diagrams](https://mlsanity.com/paper/2312.17093/) (2023)
- [Topology-Aware CLIP Few-Shot Learning](https://mlsanity.com/paper/2505.01694/) (2025)
- [The Density of Cross-Persistence Diagrams and Its Applications](https://mlsanity.com/paper/2603.11623/) (2026)
- [Pool-Based Active Learning with Proper Topological Regions](https://mlsanity.com/paper/2310.01597/) (2023)
- [Neural Persistence Dynamics](https://mlsanity.com/paper/2405.15732/) (2024)
- [TopOC: Topological Deep Learning for Ovarian and Breast Cancer Diagnosis](https://mlsanity.com/paper/2410.09818/) (2024)
- [Conformable Convolution for Topologically Aware Learning of Complex Anatomical Structures](https://mlsanity.com/paper/2412.20608/) (2024)
- [Using Graph Convolutional Networks to Address fMRI Small Data Problems](https://mlsanity.com/paper/2502.17489/) (2025)
- [Learning Topology-Aware Representations via Test-Time Adaptation for Anomaly Segmentation](https://mlsanity.com/paper/2606.28268/) (2026)
- [A differentiability framework for zigzag persistent homology via linear interpolation](https://mlsanity.com/paper/2609.39242/) (2026)

## Abstract (arXiv)

Functional magnetic resonance imaging (fMRI) is a crucial technology for gaining insights into cognitive processes in humans. Data amassed from fMRI measurements result in volumetric data sets that vary over time. However, analysing such data presents a challenge due to the large degree of noise and person-to-person variation in how information is represented in the brain. To address this challenge, we present a novel topological approach that encodes each time point in an fMRI data set as a persistence diagram of topological features, i.e. high-dimensional voids present in the data. This representation naturally does not rely on voxel-by-voxel correspondence and is robust to noise. We show that these time-varying persistence diagrams can be clustered to find meaningful groupings between participants, and that they are also useful in studying within-subject brain state trajectories of subjects performing a particular task. Here, we apply both clustering and trajectory analysis techniques to a group of participants watching the movie 'Partly Cloudy'. We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.