# Persistent Homology for MCI Classification: A Comparative Analysis between Graph and Vietoris-Rips Filtrations

arXiv: https://arxiv.org/abs/2410.22681 · HTML: https://mlsanity.com/paper/2410.22681/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 41 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia](https://mlsanity.com/paper/1809.08504/) (2018)
- [Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer](https://mlsanity.com/paper/1809.06433/) (2018)
- [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)
- [Sliding Window Persistence of Quasiperiodic Functions](https://mlsanity.com/paper/2103.04540/) (2021)
- [Partial Correlations in Compositional Data Analysis](https://mlsanity.com/paper/1904.09480/) (2019)
- [Multi-scale fMRI time series analysis for understanding neurodegeneration in MCI](https://mlsanity.com/paper/2402.02811/) (2024)
- [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)

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

- [sMRI-based Brain Age Estimation in MCI using Persistent Homology](https://mlsanity.com/paper/2511.05520/) (2025)
- [Data-driven techniques for translational neuroscience and personalized neuro-health](https://mlsanity.com/paper/2608.13749/) (2026)
- [DWI Connectome-based Sex Classification in Young using Supervised Variational Autoencoder](https://mlsanity.com/paper/2610.16348/) (2026)

## Abstract (arXiv)

Mild cognitive impairment (MCI), often linked to early neurodegeneration, is characterized by subtle cognitive declines and disruptions in brain connectivity. The present study offers a detailed analysis of topological changes associated with MCI, focusing on two subtypes: Early MCI and Late MCI. This analysis utilizes fMRI time series data from two distinct populations: the publicly available ADNI dataset (Western cohort) and the in-house TLSA dataset (Indian Urban cohort). Persistent Homology, a topological data analysis method, is employed with two distinct filtration techniques - Vietoris-Rips and graph filtration-for classifying MCI subtypes. For Vietoris-Rips filtration, inter-ROI Wasserstein distance matrices between persistent diagrams are used for classification, while graph filtration relies on the top ten most persistent homology features. Comparative analysis shows that the Vietoris-Rips filtration significantly outperforms graph filtration, capturing subtle variations in brain connectivity with greater accuracy. The Vietoris-Rips filtration method achieved the highest classification accuracy of 85.7% for distinguishing between age and gender matched healthy controls and MCI, whereas graph filtration reached a maximum accuracy of 71.4% for the same task. This superior performance highlights the sensitivity of Vietoris-Rips filtration in detecting intricate topological features associated with neurodegeneration. The findings underscore the potential of persistent homology, particularly when combined with the Wasserstein distance, as a powerful tool for early diagnosis and precise classification of cognitive impairments, offering valuable insights into brain connectivity changes in MCI.