# Robust Geometric Metric Learning

arXiv: https://arxiv.org/abs/2202.11550 · HTML: https://mlsanity.com/paper/2202.11550/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 3 of 3)

- [Geometric Mean Metric Learning](https://mlsanity.com/paper/1607.05002/) (2016)
- [metric-learn: Metric Learning Algorithms in Python](https://mlsanity.com/paper/1908.04710/) (2019)
- [Simultaneous penalized M-estimation of covariance matrices using geodesically convex optimization](https://mlsanity.com/paper/1608.08126/) (2016)

## Built on by (most cited first, 3 of 3)

- [The Fisher-Rao geometry of CES distributions](https://mlsanity.com/paper/2310.01032/) (2023)
- [Classification of Buried Objects from Ground Penetrating Radar Images by using Second Order Deep Learning Models](https://mlsanity.com/paper/2410.07117/) (2024)
- [Principal Component Classification](https://mlsanity.com/paper/2210.12746/) (2022)

## Abstract (arXiv)

This paper proposes new algorithms for the metric learning problem. We start by noticing that several classical metric learning formulations from the literature can be viewed as modified covariance matrix estimation problems. Leveraging this point of view, a general approach, called Robust Geometric Metric Learning (RGML), is then studied. This method aims at simultaneously estimating the covariance matrix of each class while shrinking them towards their (unknown) barycenter. We focus on two specific costs functions: one associated with the Gaussian likelihood (RGML Gaussian), and one with Tyler's M -estimator (RGML Tyler). In both, the barycenter is defined with the Riemannian distance, which enjoys nice properties of geodesic convexity and affine invariance. The optimization is performed using the Riemannian geometry of symmetric positive definite matrices and its submanifold of unit determinant. Finally, the performance of RGML is asserted on real datasets. Strong performance is exhibited while being robust to mislabeled data.