# The Mahalanobis distance for functional data with applications to classification

arXiv: https://arxiv.org/abs/1304.4786 · HTML: https://mlsanity.com/paper/1304.4786/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2013.

## Built on by (most cited first, 9 of 9)

- [A Survey of Computer Vision Technologies In Urban and Controlled-environment Agriculture](https://mlsanity.com/paper/2210.11318/) (2022)
- [Deep Neural Network Classifier for Multi-dimensional Functional Data](https://mlsanity.com/paper/2205.08592/) (2022)
- [Multi-Domain Few-Shot Learning and Dataset for Agricultural Applications](https://mlsanity.com/paper/2109.09952/) (2021)
- [Feature Extractor Stacking for Cross-domain Few-shot Learning](https://mlsanity.com/paper/2205.05831/) (2022)
- [Multiclass classification for multidimensional functional data through deep neural networks](https://mlsanity.com/paper/2305.13349/) (2023)
- [Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detection](https://mlsanity.com/paper/2407.11873/) (2024)
- [Noisy Data Visualization using Functional Data Analysis](https://mlsanity.com/paper/2406.03396/) (2024)
- [Supervised Manifold Learning for Functional Data](https://mlsanity.com/paper/2503.17943/) (2025)
- [On What We Can Learn from Low-Resolution Data](https://mlsanity.com/paper/2605.12168/) (2026)

## Abstract (arXiv)

This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usual Mahalanobis distance for multivariate datasets is introduced. For that, the development uses a regularized square root inverse operator in Hilbert spaces. Some of the main characteristics of the functional Mahalanobis semi-distance are shown. Afterwards, new versions of several well known functional classification procedures are developed using the Mahalanobis distance for functional data as a measure of proximity between functional observations. The performance of several well known functional classification procedures are compared with those methods used in conjunction with the Mahalanobis distance for functional data, with positive results, through a Monte Carlo study and the analysis of two real data examples.