Deep neural network classifier for multidimensional functional data

Document Type

Article

Publication Date

12-1-2023

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.

Identifier

85160075490 (Scopus)

Publication Title

Scandinavian Journal of Statistics

External Full Text Location

https://doi.org/10.1111/sjos.12660

e-ISSN

14679469

ISSN

03036898

First Page

1667

Last Page

1686

Issue

4

Volume

50

Grant

DMS 1736470

Fund Ref

National Science Foundation

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