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

Debanjali Bhattacharya, Rajneet Kaur, Ninad Aithal, Neelam Sinha, Thomas Gregor Issac

TL;DR

Vietoris-Rips filtration is highlighted, offering a robust tool for early diagnosis and precise classification of MCI subtypes, and significantly outperforms graph filtration in brain network analysis.

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.

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

TL;DR

Vietoris-Rips filtration is highlighted, offering a robust tool for early diagnosis and precise classification of MCI subtypes, and significantly outperforms graph filtration in brain network analysis.

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.

Paper Structure

This paper contains 26 sections, 5 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Dataset Description
  4. Overview on Proposed Methodology
  5. Extraction of fMRI time series
  6. Persistent homology using Vietoris-Rips filtration
  7. Persistent homology using graph filtration
  8. Graph construction using marginal and partial correlation
  9. Graph Filtration
  10. Quantification of persistence diagrams using Wasserstein distance
  11. Network-Specific Inter-Subject Wasserstein distance
  12. Subject-Specific Inter-ROI Wasserstein distance
  13. Classification
  14. Stacked Ensemble Classifier
  15. Proposed CNN framework
  16. ...and 11 more sections

Figures (5)

  • Figure 1: Block diagram showing the Proposed Methodology.
  • Figure 2: Image showing Dosenbach’s ROIs for the six networks.
  • Figure 3: The persistence barcode for a representative subject for Healthy, EMCI and LMCI group for network OP.
  • Figure 4: The deep learning architecture for classification using persistent diagrams generated with Vietoris-Rips filtration
  • Figure 5: Illustration of the comparative analysis between graph filtration and Vietoris-Rips filtration for both dimension-0 $(H_{0})$ and dimension-1 $(H_{1})$ in the classification of (A) healthy controls (HC) versus early mild cognitive impairment (EMCI), (B) HC versus late mild cognitive impairment (LMCI), (C) EMCI versus LMCI, and (D) HC versus mild cognitive impairment (MCI) based on TLSA data. The plot clearly highlights the superiority of Vietoris-Rips filtration over graph filtration, showcasing its enhanced ability to differentiate between these cognitive states.