Penalized discriminant analysis for multivariate functional data

Abstract

We introduce a penalized discriminant analysis method for multivariate functional data supported on compact 1D domains, motivated by an application that aims to identify subjects with poor cognitive status from diffusion MRI data. By leveraging a connection to the optimal scoring problem, we bypass minimizing complex objective functions directly and recast the problem into a penalized regression framework. The proposed formulation leads to an efficient model. The classifier achieved adequate prediction performance on the challenging diffusion MRI dataset. Simulation studies showed that the univariate classifier achieves satisfactory performance compared to existing methods. As an extension of the methodology proposed, we also present a multi-class classifier that can accommodate multiple outcome categories.