# Supervised Manifold Learning for Functional Data

arXiv: https://arxiv.org/abs/2503.17943 · HTML: https://mlsanity.com/paper/2503.17943/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 50 references that are in the map.
- First posted on arXiv 23 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Functional Data Analysis of Amplitude and Phase Variation](https://mlsanity.com/paper/1512.03216/) (2015)
- [The Mahalanobis distance for functional data with applications to classification](https://mlsanity.com/paper/1304.4786/) (2013)
- [Parallel Transport Unfolding: A Connection-based Manifold Learning Approach](https://mlsanity.com/paper/1806.09039/) (2018)
- [Optimal Bayes Classifiers for Functional Data and Density Ratios](https://mlsanity.com/paper/1605.03707/) (2016)
- [Deep Neural Network Classifier for Multi-dimensional Functional Data](https://mlsanity.com/paper/2205.08592/) (2022)
- [On the use of reproducing kernel Hilbert spaces in functional classification](https://mlsanity.com/paper/1507.04398/) (2015)
- [Classification of functional fragments by regularized linear classifiers with domain selection](https://mlsanity.com/paper/1708.08257/) (2017)
- [Optimal Classification for Functional Data](https://mlsanity.com/paper/2103.00569/) (2021)

## Abstract (arXiv)

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In contrast, we investigate this topic from the perspective of manifold learning. It is assumed that functional data lie on an unknown low-dimensional manifold, and we expect that superior classifiers can be developed based on the manifold structure. To this end, we propose a novel proximity measure that takes the label information into account to learn the low-dimensional representations, also known as the supervised manifold learning outcomes. When the outcomes are coupled with multivariate classifiers, the procedure induces a new family of functional classifiers. In theory, we prove that our functional classifier induced by the k-NN classifier is asymptotically optimal. In practice, we show that our method, coupled with several classical multivariate classifiers, achieves highly competitive classification performance compared to existing functional classifiers across both synthetic and real data examples. Supplementary materials are available online.