Topological Data Analysis-Driven fNIRS Signal Processing for Alzheimer’s Disease Stage Identification

This paper proposes a novel Topological Data Analysis (TDA) pipeline to extract robust structural features from functional near-infrared spectroscopy (fNIRS) signals for the classification of Alzheimer's Disease (AD) stages. Alzheimer's disease is increasingly understood as a disconnection syndrome, where the disruption of functional brain net-works precedes gross anatomical atrophy. However, traditional graph-theoretic ap-proaches rely on arbitrary connectivity thresholds, which can obscure critical multi-scale topological information and are sensitive to noise. To address this, our framework lev-erages Persistent Homology (PH) to analyse the topological evolution of brain networks across a continuous range of scales. By modeling 48-channel hemoglobin concentration time-series as high-dimensional point clouds via Granger causality metrics, we construct filtration sequences of Vietoris-Rips complexes. The resulting topological invari-ants—specifically 0-dimensional connected components, 1-dimensional loops, and 2-dimensional voids—are captured in Persistence Diagrams and subsequently vectorized into Persistence Images (PIs) using Gaussian kernel smoothing. This transformation enables the integration of complex topological features into standard machine learning workflows. Our experimental results on 284 recordings demonstrate that this topolo-gy-driven feature extraction method yields high discriminative power, achieving 77% accuracy in multi-class diagnosis (NC vs. MCI vs. AD). This study validates the efficacy of TDA as a sophisticated signal processing tool for revealing intrinsic neurodegenerative patterns in hemodynamic data, offering a potential non-invasive biomarker for early detection.