mlsanityData to 7 Oct 2026

Deep Neural Network Classifier for Multi-dimensional Functional Data

arXiv 2205.08592 ↗First posted 17 May 2022stat.ML cs.LG stat.MEcited by 5

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Abstract (arXiv)

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.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 20 of its 43 references that are in the map. First posted on arXiv 17 May 2022.

Builds on

20 of 43 references.

References · 20

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8 more
  1. 2013The Mahalanobis distance for functional data with applications to classificationcited by 9
  2. 2019Optimal Nonparametric Inference via Deep Neural Networkcited by 9
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 0; 2025: 2; 2026: 1.

5 papers.

  1. 2025DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classificationcited by 3
  2. 2023Semiparametric Regression for Spatial Data via Deep Learningcited by 2
  3. 2023Nonparametric Classification on Low Dimensional Manifolds using Overparameterized Convolutional Residual Networkscited by 2
  4. 2025Supervised Manifold Learning for Functional Datacited by 0
  5. 2026Sparse Bayesian Deep Functional Learning with Structured Region Selectioncited by 0