# Geometric statistics with subspace structure preservation for SPD matrices

arXiv: https://arxiv.org/abs/2407.03382 · HTML: https://mlsanity.com/paper/2407.03382/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 12 references that are in the map.
- First posted on arXiv 2 Jul 2024.

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

- [Differential geometry with extreme eigenvalues in the positive semidefinite cone](https://mlsanity.com/paper/2304.07347/) (2023)
- [Geometric Matrix Midranges](https://mlsanity.com/paper/1907.04188/) (2019)
- [Inductive Geometric Matrix Midranges](https://mlsanity.com/paper/2006.01508/) (2020)

## Abstract (arXiv)

We present a geometric framework for the processing of SPD-valued data that preserves subspace structures and is based on the efficient computation of extreme generalized eigenvalues. This is achieved through the use of the Thompson geometry of the semidefinite cone. We explore a particular geodesic space structure in detail and establish several properties associated with it. Finally, we review a novel inductive mean of SPD matrices based on this geometry.