Open Access
2024 Multiclass classification for multidimensional functional data through deep neural networks
Shuoyang Wang, Guanqun Cao
Author Affiliations +
Electron. J. Statist. 18(1): 1248-1292 (2024). DOI: 10.1214/24-EJS2229

Abstract

The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass functional deep neural network (mfDNN) classifier as an innovative data mining and classification tool. The architecture incorporates a sparse deep neural network with Rectified Linear Unit (ReLU) activation function, minimizing cross-entropy loss in a multiclass classification framework. This design enables the utilization of modern computational tools. The convergence rates of the misclassification risk functions are also derived for both fully observed and discretely observed multidimensional functional data. The efficacy of mfDNN is demonstrated through simulations and several benchmark datasets from different application domains.

Funding Statement

Cao’s research was also partially supported by the Simons Foundation under Grant #849413 and National Science Foundation under Grants CNS-2319342 and CNS-2319343.

Acknowledgments

ADNI data used in preparation of this article were obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.

Citation

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Shuoyang Wang. Guanqun Cao. "Multiclass classification for multidimensional functional data through deep neural networks." Electron. J. Statist. 18 (1) 1248 - 1292, 2024. https://doi.org/10.1214/24-EJS2229

Information

Received: 1 October 2023; Published: 2024
First available in Project Euclid: 13 March 2024

Digital Object Identifier: 10.1214/24-EJS2229

Subjects:
Primary: 62G05 , 62G08
Secondary: 62G35

Keywords: Deep neural networks , Functional data analysis , Multiclass classification , multidimensional functional data , rate of convergence

Vol.18 • No. 1 • 2024
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