Title: Interpretable discriminant analysis for functional data supported on general random domains
Authors: Eardi Lila - University of Washington (United States) [presenting]
Abstract: A novel framework is introduced for the classification of functional data supported on non-linear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer's disease from their cortical surface geometry and associated cortical thickness map. The proposed model is based upon a reformulation of the classification problem into a regularized multivariate functional linear regression model. This allows us to directly estimate the discriminant direction while controlling for its complexity with appropriate differential regularizations. The approach does not require prior estimation of the covariance structure of the functional predictors, which is computationally not feasible in our application setting. We apply the proposed method to the Alzheimer's Disease Neuroimaging Initiative data and are able to estimate novel discriminant directions that capture both geometric and thickness predictive features of the cerebral cortex.