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 networks precedes gross anatomical atrophy. However, traditional graph-theoretic approaches rely on arbitrary connectivity thresholds, which can obscure critical multi-scale topological information, and are sensitive to noise. To address this, our framework leverages 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 invariants, including 0-dimensional connected components, 1-dimensional loops, and 2-dimensional voids, are first examined through Persistence Diagrams. For classification, significant H0 and H1 features are converted into Persistence Images using Gaussian kernel smoothing, while H2 features are retained for qualitative topological interpretation. This transformation enables the integration of complex topological features into standard machine learning workflows. Our experimental results were evaluated on a subject-level held-out test set consisting only of original, non-augmented recordings. Data augmentation was applied only to the training set to alleviate class imbalance. The proposed topology-driven feature extraction method achieved 86% 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 an exploratory methodological proof-of-concept for AD stage classification.