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Title: Deep neural network classifier for multi-dimensional functional data Authors:  Guanqun Cao - Auburn University (United States) [presenting]
Zuofeng Shang - New Jersey Institute of Technology (United States)
Abstract: A new approach is proposed, called functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data, which shall be used to predict the class label of a future data function. Unlike the popular functional discriminant analysis approaches, which rely on Gaussian assumption, the proposed FDNN approach applies to general non-Gaussian multi-dimensional functional data. Moreover, when the log density ratio possesses a locally connected functional modular structure, we show that FDNN achieves minimax optimality. The superiority of our approach is demonstrated through both simulated and real-world datasets.