# Directional Statistics in Machine Learning: a Brief Review

arXiv: https://arxiv.org/abs/1605.00316 · HTML: https://mlsanity.com/paper/1605.00316/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2016.

## Built on by (most cited first, 13 of 13)

- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [Learning Riemannian Manifolds for Geodesic Motion Skills](https://mlsanity.com/paper/2106.04315/) (2021)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstruction](https://mlsanity.com/paper/2301.04791/) (2023)
- [Reactive Motion Generation on Learned Riemannian Manifolds](https://mlsanity.com/paper/2203.07761/) (2022)
- [ComFe: An Interpretable Head for Vision Transformers](https://mlsanity.com/paper/2403.04125/) (2024)
- [Dynamic Feature Learning and Matching for Class-Incremental Learning](https://mlsanity.com/paper/2405.08533/) (2024)
- [Kuramoto Oscillators and Swarms on Manifolds for Geometry Informed Machine Learning](https://mlsanity.com/paper/2405.09453/) (2024)
- [Von Mises-Fisher Elliptical Distribution](https://mlsanity.com/paper/2103.07948/) (2021)
- [Weak Supervision in Analysis of News: Application to Economic Policy Uncertainty](https://mlsanity.com/paper/2209.05383/) (2022)
- [Precise Bayesian Neural Networks](https://mlsanity.com/paper/2506.19726/) (2025)
- [Relation-Aware Slicing in Cross-Domain Alignment](https://mlsanity.com/paper/2507.13194/) (2025)
- [Angular Regularization for Positive-Unlabeled Learning on the Hypersphere](https://mlsanity.com/paper/2512.06785/) (2025)

## Abstract (arXiv)

The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data encoded as normalized vectors, so that their "direction" is more important than their magnitude. Specifically, we consider high-dimensional vectors that lie either on the surface of the unit hypersphere or on the real projective plane. For such data, we briefly review common mathematical models prevalent in machine learning, while also outlining some technical aspects, software, applications, and open mathematical challenges.