# Multiclass classification for multidimensional functional data through deep neural networks

arXiv: https://arxiv.org/abs/2305.13349 · HTML: https://mlsanity.com/paper/2305.13349/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 14 of 14)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Fast convergence rates of deep neural networks for classification](https://mlsanity.com/paper/1812.03599/) (2018)
- [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)
- [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)
- [Multiclass Sparse Discriminant Analysis](https://mlsanity.com/paper/1504.05845/) (2015)
- [Estimation of the Mean Function of Functional Data via Deep Neural Networks](https://mlsanity.com/paper/2012.04573/) (2020)
- [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)
- [Bayesian Classification of Multiclass Functional Data](https://mlsanity.com/paper/1808.00662/) (2018)
- [Optimal Classification for Functional Data](https://mlsanity.com/paper/2103.00569/) (2021)

## Built on by (most cited first, 1 of 1)

- [DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classification](https://mlsanity.com/paper/2501.18116/) (2025)

## Abstract (arXiv)

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. Specifically, we consider sparse deep neural network architecture with rectifier linear unit (ReLU) activation function and minimize the cross-entropy loss in the multiclass classification setup. This neural network architecture allows us to employ modern computational tools in the implementation. The convergence rates of the misclassification risk functions are also derived for both fully observed and discretely observed multidimensional functional data. We demonstrate the performance of mfDNN on simulated data and several benchmark datasets from different application domains.