Deep Neural Network Classifier for Multi-dimensional Functional Data

• URL: http://arxiv.org/abs/2205.08592v1
• Date: Tue, 17 May 2022 19:22:48 GMT
• Title: Deep Neural Network Classifier for Multi-dimensional Functional Data
• Authors: Shuoyang Wang, Guanqun Cao, Zuofeng Shang
• Abstract summary: 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.
• Score: 4.340040784481499
• License: http://creativecommons.org/licenses/by/4.0/
• 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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