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

TL;DR

This study compares two topological data analysis methods, Vietoris-Rips and graph filtration, using persistent homology to classify MCI subtypes from fMRI data, finding Vietoris-Rips significantly more accurate.

Contribution

It demonstrates the superior effectiveness of Vietoris-Rips filtration over graph filtration in classifying MCI using persistent homology on brain connectivity data.

Findings

Vietoris-Rips filtration achieved 85.7% accuracy in MCI classification.

Graph filtration reached a maximum of 71.4% accuracy.

Vietoris-Rips filtration better captures subtle brain connectivity changes.

Abstract

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.