Hyperbolic Space Sparse Coding with Its Application on Prediction of Alzheimer's Disease in Mild Cognitive Impairment

Mild Cognitive Impairment (MCI) is a transitional stage between normal age-related cognitive decline and Alzheimer's disease (AD). Here we introduce a hyperbolic space sparse coding method to predict impending decline of MCI patients to dementia using surface measures of ventricular enlargement. First, we compute diffeomorphic mappings between ventricular surfaces using a canonical hyperbolic parameter space with consistent boundary conditions and surface tensor-based morphometry is computed to measure local surface deformations. Second, ring-shaped patches of TBM features are selected according to the geometric structure of the hyperbolic parameter space to initialize a dictionary. Sparse coding is then applied on the patch features to learn sparse codes and update the dictionary. Finally, we adopt max-pooling to reduce the feature dimensions and apply Adaboost to predict AD in MCI patients (N = 133) from the Alzheimer's Disease Neuroimaging Initiative baseline dataset. Our work achieved an accuracy rate of 96.7% and outperformed some other morphometry measures. The hyperbolic space sparse coding method may offer a more sensitive tool to study AD and its early symptom.