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

Jie Zhang, Jie Shi, Cynthia Stonnington, Qingyang Li, Boris A. Gutman, Kewei Chen, Eric M. Reiman, Richard Caselli, Paul M. Thompson, Jieping Ye, Yalin Wang


Abstract

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.

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