# Deep Neural Network Classifier for Multi-dimensional Functional Data

arXiv: https://arxiv.org/abs/2205.08592 · HTML: https://mlsanity.com/paper/2205.08592/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 17 May 2022.

## Builds on (most cited first, 20 of 20)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Optimal approximation of piecewise smooth functions using deep ReLU neural networks](https://mlsanity.com/paper/1709.05289/) (2017)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Fast convergence rates of deep neural networks for classification](https://mlsanity.com/paper/1812.03599/) (2018)
- [A Minimax Approach to Supervised Learning](https://mlsanity.com/paper/1606.02206/) (2016)
- [Convergence rates of deep ReLU networks for multiclass classification](https://mlsanity.com/paper/2108.00969/) (2021)
- [High-dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm, and Missing Data](https://mlsanity.com/paper/1804.03018/) (2018)
- [On Deep Instrumental Variables Estimate](https://mlsanity.com/paper/2004.14954/) (2020)
- [Sharp Rate of Convergence for Deep Neural Network Classifiers under the Teacher-Student Setting](https://mlsanity.com/paper/2001.06892/) (2020)
- [Minimax Classification with 0-1 Loss and Performance Guarantees](https://mlsanity.com/paper/2010.07964/) (2020)
- [A Convex Optimization Approach to High-Dimensional Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1912.02872/) (2019)
- [The Mahalanobis distance for functional data with applications to classification](https://mlsanity.com/paper/1304.4786/) (2013)
- [Optimal Nonparametric Inference via Deep Neural Network](https://mlsanity.com/paper/1902.01687/) (2019)
- [Estimation of the Mean Function of Functional Data via Deep Neural Networks](https://mlsanity.com/paper/2012.04573/) (2020)
- [Calibrating multi-dimensional complex ODE from noisy data via deep neural networks](https://mlsanity.com/paper/2106.03591/) (2021)
- [Optimal Bayes Classifiers for Functional Data and Density Ratios](https://mlsanity.com/paper/1605.03707/) (2016)
- [On the use of reproducing kernel Hilbert spaces in functional classification](https://mlsanity.com/paper/1507.04398/) (2015)
- [Mixture model-based functional discriminant analysis for curve classification](https://mlsanity.com/paper/1312.7018/) (2013)
- [Sparse Functional Linear Discriminant Analysis](https://mlsanity.com/paper/2012.06488/) (2020)

## Built on by (most cited first, 5 of 5)

- [DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classification](https://mlsanity.com/paper/2501.18116/) (2025)
- [Semiparametric Regression for Spatial Data via Deep Learning](https://mlsanity.com/paper/2301.03747/) (2023)
- [Nonparametric Classification on Low Dimensional Manifolds using Overparameterized Convolutional Residual Networks](https://mlsanity.com/paper/2307.01649/) (2023)
- [Supervised Manifold Learning for Functional Data](https://mlsanity.com/paper/2503.17943/) (2025)
- [Sparse Bayesian Deep Functional Learning with Structured Region Selection](https://mlsanity.com/paper/2602.20651/) (2026)

## 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.