# A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds

arXiv: https://arxiv.org/abs/2111.15371 · HTML: https://mlsanity.com/paper/2111.15371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2021.

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

- [Sasaki Metric for Spline Models of Manifold-Valued Trajectories](https://mlsanity.com/paper/2303.17299/) (2023)
- [Predicting Shape Development: a Riemannian Method](https://mlsanity.com/paper/2212.04740/) (2022)
- [Ridge Regression on Riemannian Manifolds for Time-Series Prediction](https://mlsanity.com/paper/2411.18339/) (2024)

## Abstract (arXiv)

In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.