Multiclass Classification for Multidimensional Functional Data Through Deep Neural Networks

The intrinsically infinite -dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass functional deep neural network (mfDNN) classifier as an innovative data mining and classification tool. The architecture incorporates a sparse deep neural network with Rectified Linear Unit (ReLU) activation function, minimizing cross -entropy loss in a multiclass classification framework. This design enables the utilization of modern computational tools. The convergence rates of the misclassification risk functions are also derived for both fully observed and discretely observed multidimensional functional data. The efficacy of mfDNN is demonstrated through simulations and several benchmark datasets from different application domains.