# Depth for curve data and applications

arXiv: https://arxiv.org/abs/1901.00180 · HTML: https://mlsanity.com/paper/1901.00180/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2019.

## Built on by (most cited first, 8 of 8)

- [A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regions](https://mlsanity.com/paper/2103.12711/) (2021)
- [Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth](https://mlsanity.com/paper/2202.08789/) (2022)
- [Statistical Depth Functions for Ranking Distributions: Definitions, Statistical Learning and Applications](https://mlsanity.com/paper/2201.08105/) (2022)
- [Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications](https://mlsanity.com/paper/2111.03217/) (2021)
- [Anomaly detection using data depth: multivariate case](https://mlsanity.com/paper/2210.02851/) (2022)
- [Nonparametric plug-in classifier for multiclass classification of S.D.E. paths](https://mlsanity.com/paper/2212.10259/) (2022)
- [Empirical risk minimization algorithm for multiclass classification of S.D.E. paths](https://mlsanity.com/paper/2503.14045/) (2025)
- [Model-Free Kernel Conformal Depth Measures Algorithm for Uncertainty Quantification in Regression Models in Separable Hilbert Spaces](https://mlsanity.com/paper/2506.08325/) (2025)

## Abstract (arXiv)

John W. Tukey (1975) defined statistical data depth as a function that determines centrality of an arbitrary point with respect to a data cloud or to a probability measure. During the last decades, this seminal idea of data depth evolved into a powerful tool proving to be useful in various fields of science. Recently, extending the notion of data depth to the functional setting attracted a lot of attention among theoretical and applied statisticians. We go further and suggest a notion of data depth suitable for data represented as curves, or trajectories, which is independent of the parametrization. We show that our curve depth satisfies theoretical requirements of general depth functions that are meaningful for trajectories. We apply our methodology to diffusion tensor brain images and also to pattern recognition of hand written digits and letters. Supplementary Materials are available online.