Persistent homology for MCI classification: a comparative analysis between graph and Vietoris-Rips filtrations

Introduction: Mild cognitive impairment (MCI), often linked to early neurodegeneration, is associated with subtle disruptions in brain connectivity. In this paper, the applicability of persistent homology, a cutting-edge topological data analysis technique is explored for classifying MCI subtypes. Method: The study examines 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. Result: 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. Discussion: 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.