Topological Data Analysis for Early Detection of Neurodegenerative Disease

Abstract: Neurodegenerative diseases, such as Alzheimer's and Parkinson's, are characterized by progressive neuronal deterioration, leading to cognitive and motor impairments. Early detection is crucial for effective intervention and management. This study proposes a novel framework utilizing Topological Data Analysis (TDA), particularly persistent homology, to identify early biomarkers from neuroimaging and physiological data. This study explores the application of TDA techniques—specifically persistent homology and topological invariants—for the early detection of neurodegenerative diseases such as Alzheimer's. By analyzing functional brain connectivity, gait dynamics, and molecular structures associated with disease progression, the research demonstrates that TDA can capture subtle, yet critical, topological signatures indicative of early neurodegenerative changes. Layer-wise topological complexity in neural networks and persistent homology in clinical datasets reveal distinct structural degradation patterns. The integration of TDA with machine learning models enhances diagnostic accuracy, interpretability, and generalization, offering a promising direction for non-invasive, data-driven diagnostics in neurology.By capturing the intrinsic topological features of brain networks, the framework aims to distinguish between healthy and early-stage neurodegenerative conditions, offering a robust tool for early diagnosis.Topological Data Analysis (TDA) offers a robust mathematical framework for extracting shape-based features from high-dimensional and noisy biomedical data. Keywords: Topological Data Analysis, Persistent Homology, Neurodegenerative Disease, Alzheimer's, Brain Connectivity, Early Diagnosis, Betti Numbers, Gait Analysis, Functional Networks, Machine Learning, Biomedical Data