Interpretable discriminant analysis for functional data supported on random nonlinear domains with an application to Alzheimer's disease

• 成果类型: Article; Early Access
• 署名作者: Lila, Eardi; Zhang, Wenbo; Levendovszky, Swati Rane
• 署名单位: University of Washington; University of Washington Seattle; University of California System; University of California Irvine; University of Washington; University of Washington Seattle
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae023
• 发表日期: 2024
• 关键词: Principal component analysis; surface-based analysis; kernel hilbert-spaces; human cerebral-cortex; on-image regression; RIEMANNIAN-MANIFOLDS; cortical surface; shape-analysis; CLASSIFICATION; prediction

摘要

We introduce a novel framework for the classification of functional data supported on nonlinear, 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 as a regularized multivariate functional linear regression model. This allows us to adopt a direct approach to the estimation of the most discriminant direction while controlling for its complexity with appropriate differential regularization. Our approach does not require prior estimation of the covariance structure of the functional predictors, which is computationally prohibitive in our application setting. We provide a theoretical analysis of the out-of-sample prediction error of the proposed model and explore the finite sample performance in a simulation setting. We apply the proposed method to a pooled dataset from Alzheimer's Disease Neuroimaging Initiative and Parkinson's Progression Markers Initiative. Through this application, we identify discriminant directions that capture both cortical geometric and thickness predictive features of Alzheimer's disease that are consistent with the existing neuroscience literature.