# Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia

arXiv: https://arxiv.org/abs/1809.08504 · HTML: https://mlsanity.com/paper/1809.08504/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2018.

## Built on by (most cited first, 10 of 10)

- [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)
- [Image complexity based fMRI-BOLD visual network categorization across visual datasets using topological descriptors and deep-hybrid learning](https://mlsanity.com/paper/2311.08417/) (2023)
- [Analyzing Brain Tumor Connectomics using Graphs and Persistent Homology](https://mlsanity.com/paper/2407.17938/) (2024)
- [Leveraging Persistent Homology for Differential Diagnosis of Mild Cognitive Impairment](https://mlsanity.com/paper/2408.15647/) (2024)
- [Persistent Homology for MCI Classification: A Comparative Analysis between Graph and Vietoris-Rips Filtrations](https://mlsanity.com/paper/2410.22681/) (2024)
- [Topological EEG Nonlinear Dynamics Analysis for Emotion Recognition](https://mlsanity.com/paper/2203.06895/) (2022)
- [From augmented microscopy to the topological transformer: a new approach in cell image analysis for Alzheimer's research](https://mlsanity.com/paper/2108.01625/) (2021)
- [Hypergraphs on high dimensional time series sets using signature transform](https://mlsanity.com/paper/2507.15802/) (2025)

## Abstract (arXiv)

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using k-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions.