# Bayesian Geodesic Regression on Riemannian Manifolds

arXiv: https://arxiv.org/abs/2009.05108 · HTML: https://mlsanity.com/paper/2009.05108/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Deep Extrinsic Manifold Representation for Vision Tasks](https://mlsanity.com/paper/2404.00544/) (2024)

## Abstract (arXiv)

Geodesic regression has been proposed for fitting the geodesic curve. However, it cannot automatically choose the dimensionality of data. In this paper, we develop a Bayesian geodesic regression model on Riemannian manifolds (BGRM) model. To avoid the overfitting problem, we add a regularization term to control the effectiveness of the model. To automatically select the dimensionality, we develop a prior for the geodesic regression model, which can automatically select the number of relevant dimensions by driving unnecessary tangent vectors to zero. To show the validation of our model, we first apply it in the 3D synthetic sphere and 2D pentagon data. We then demonstrate the effectiveness of our model in reducing the dimensionality and analyzing shape variations of human corpus callosum and mandible data.