Empowering Multi-class Classification for Multivariate Functional Data with Simultaneous Feature Selection

The opportunity to utilize complex functional data types for conducting classification tasks is emerging with the growing availability of imaging data. However, the tools capable of effectively managing imaging data are limited, let alone those that can further leverage other one-dimensional functional data. Inspired by the extensive data provided by the Alzheimer's Disease Neuroimaging Initiative (ADNI), we introduce a novel classifier tailored for complex 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 p can potentially be much greater than the sample size n. In this paper, we introduce a novel and scalable classifier termed functional BIC deep neural network. By adopting a sparse deep Rectified Linear Unit network architecture and incorporating the LassoNet algorithm, the proposed unified model performs feature selection and classification simultaneously, which is contrast to the existing functional data classifiers. The challenge arises from the complex inter-correlation structures among multiple functional processes, and at meanwhile without any assumptions on the distribution of these processes. Simulation study and real data application are carried out to demonstrate its favorable performance.