# Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces

arXiv: https://arxiv.org/abs/2102.07771 · HTML: https://mlsanity.com/paper/2102.07771/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 16 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 1 of 1)

- [Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels](https://mlsanity.com/paper/2011.13680/) (2020)

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

- [Differential geometry with extreme eigenvalues in the positive semidefinite cone](https://mlsanity.com/paper/2304.07347/) (2023)
- [Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm](https://mlsanity.com/paper/2207.00818/) (2022)
- [Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices](https://mlsanity.com/paper/2203.00204/) (2022)

## Abstract (arXiv)

Hidden Markov models with observations in a Euclidean space play an important role in signal and image processing. Previous work extending to models where observations lie in Riemannian manifolds based on the Baum-Welch algorithm suffered from high memory usage and slow speed. Here we present an algorithm that is online, more accurate, and offers dramatic improvements in speed and efficiency.