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Deep neural network classifier for multidimensional functional data

Author

Listed:
  • Shuoyang Wang
  • Guanqun Cao
  • Zuofeng Shang
  • for the Alzheimer's Disease Neuroimaging Initiative

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.

Suggested Citation

  • Shuoyang Wang & Guanqun Cao & Zuofeng Shang & for the Alzheimer's Disease Neuroimaging Initiative, 2023. "Deep neural network classifier for multidimensional functional data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1667-1686, December.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:4:p:1667-1686
    DOI: 10.1111/sjos.12660
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    References listed on IDEAS

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    4. Aurore Delaigle & Peter Hall, 2013. "Classification Using Censored Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1269-1283, December.
    5. José R. Berrendero & Antonio Cuevas & José L. Torrecilla, 2018. "On the Use of Reproducing Kernel Hilbert Spaces in Functional Classification," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1210-1218, July.
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