Deep Neural Network Classifier for Multi-dimensional Functional Data

Shuoyang Wang; Guanqun Cao; Zuofeng Shang

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arXiv · 2205.08592

Deep Neural Network Classifier for Multi-dimensional Functional Data

Shuoyang Wang·Guanqun Cao·Zuofeng Shang

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Abstract

We propose a new approach, called as 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.

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Shuoyang Wang, Guanqun Cao, Zuofeng Shang. 2022-05-17. Deep Neural Network Classifier for Multi-dimensional Functional Data. https://arxiv.org/abs/2205.08592

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