# Directional Outlyingness for Multivariate Functional Data

arXiv: https://arxiv.org/abs/1612.04615 · HTML: https://mlsanity.com/paper/1612.04615/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2016.

## Built on by (most cited first, 4 of 4)

- [scikit-fda: A Python Package for Functional Data Analysis](https://mlsanity.com/paper/2211.02566/) (2022)
- [Outlier detection in multivariate functional data through a contaminated mixture model](https://mlsanity.com/paper/2106.07222/) (2021)
- [A geometric perspective on functional outlier detection](https://mlsanity.com/paper/2109.06849/) (2021)
- [3D-CSAD: Untrained 3D Anomaly Detection for Complex Manufacturing Surfaces](https://mlsanity.com/paper/2404.07748/) (2024)

## Abstract (arXiv)

The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical properties of functional directional outlyingness and find that the total outlyingness can be naturally decomposed into two parts: magnitude outlyingness and shape outlyingness which represent the centrality of a curve for magnitude and shape, respectively. Using this decomposition, we provide a visualization tool for the centrality of curves. Furthermore, we design an outlier detection procedure based on functional directional outlyingness. This criterion applies to both univariate and multivariate curves and simulation studies show that it outperforms competing methods. Weather and electrocardiogram data demonstrate the practical application of our proposed framework.