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

Debanjali Bhattacharya ^1* Rajneet Kaur ^1* Ninad Aithal ² Neelam Sinha ^1* Thomas Gregor ^1*

• ¹ Centre for Brain Research, Indian Institute of Science, Bangalore, Karnataka, India
• ² Indian Institute of Science (IISc), Bangalore, Karnataka, India

Mild cognitive impairment (MCI), often linked to early neurodegeneration, is associated with subtle disruptions in brain connectivity. The present study explores the applicability of persistent homology, a cutting-edge topological data analysis technique, for classifying MCI subtypes. This is done by examining brain network topology derived from fMRI time series data. In this regard, we investigate two methods for computing persistent homology: (1) Vietoris-Rips filtration, which leverages point clouds generated from fMRI time series to capture dynamic and global changes in brain connectivity, and (2) graph filtration, which examines connectivity matrices based on static pairwise correlations. The obtained persistent topological features are quantified using Wasserstein distance, which enables a detailed comparison of brain network structures. Our findings show that Vietoris-Rips filtration significantly outperforms graph filtration in brain network analysis. Specifically, it achieves a maximum accuracy of 85.7% in the Default Mode Network, for classifying MCI using in-house dataset. This study highlights the superior ability of Vietoris-Rips filtration to capture intricate brain network patterns, offering a robust tool for early diagnosis and precise classification of MCI subtypes.