Empowering classification for multivariate functional data with simultaneous feature selection

The opportunity to utilize multivariate functional data types for conducting classification tasks is emerging with the growing availability of imaging data. Inspired by the extensive data provided by the Alzheimer's Disease Neuroimaging Initiative, we introduce a novel classifier tailored for multivariate functional data. Each observation in this framework may be associated with numerous functional processes, varying in dimensions, such as curves and images. Each predictor is a random element in an infinite-dimensional function space, and the number of functional predictors can potentially be much greater than the sample size. By adopting a sparse deep rectified linear unit network architecture and incorporating the LassoNet algorithm, the proposed functional Bayesian information criterion deep neural network performs feature selection and classification simultaneously, in contrast to existing functional data classifiers. This approach addresses the challenge of complex inter-correlation structures among multiple functional processes without requiring distributional assumptions. A simulation study and a real data application demonstrate its favorable performance.