# Sasaki Metric for Spline Models of Manifold-Valued Trajectories

arXiv: https://arxiv.org/abs/2303.17299 · HTML: https://mlsanity.com/paper/2303.17299/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 30 Mar 2023.

## Builds on (most cited first, 5 of 5)

- [Geodesic analysis in Kendall's shape space with epidemiological applications](https://mlsanity.com/paper/1906.11950/) (2019)
- [Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic B'ezier Splines](https://mlsanity.com/paper/2007.05275/) (2020)
- [Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations](https://mlsanity.com/paper/2009.07427/) (2020)
- [A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds](https://mlsanity.com/paper/2202.01180/) (2022)
- [A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds](https://mlsanity.com/paper/2111.15371/) (2021)

## Built on by (most cited first, 2 of 2)

- [Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs](https://mlsanity.com/paper/2401.14381/) (2024)
- [Ridge Regression on Riemannian Manifolds for Time-Series Prediction](https://mlsanity.com/paper/2411.18339/) (2024)

## Abstract (arXiv)

We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical model. Particularly, utilizing regression, we represent discrete trajectories in a Riemannian manifold by composite B' ezier splines, propose a natural metric induced by the Sasaki metric to compare the trajectories, and estimate average trajectories as group-wise trends. We evaluate our framework in comparison to state-of-the-art methods within qualitative and quantitative experiments on hurricane tracks. Notably, our results demonstrate the superiority of spline-based approaches for an intensity classification of the tracks.