Deep neural network classifier for multidimensional functional data

Shuoyang Wang, Guanqun Cao, Zuofeng Shang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We propose a new approach, called as functional deep neural network (FDNN), for classifying multidimensional functional data. Specifically, a deep neural network is trained based on the principal 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 only work for one-dimensional functional data, the proposed FDNN approach applies to general non-Gaussian multidimensional 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.

Original languageEnglish (US)
Pages (from-to)1667-1686
Number of pages20
JournalScandinavian Journal of Statistics
Volume50
Issue number4
DOIs
StatePublished - Dec 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Minimax excess misclassification risk
  • functional classification
  • functional data analysis
  • functional neural networks
  • multidimensional functional data

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