# Probabilistic Riemannian submanifold learning with wrapped Gaussian process latent variable models

arXiv: https://arxiv.org/abs/1805.09122 · HTML: https://mlsanity.com/paper/1805.09122/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 4 of 4)

- [Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels](https://mlsanity.com/paper/2110.14423/) (2021)
- [Implicit Gaussian process representation of vector fields over arbitrary latent manifolds](https://mlsanity.com/paper/2309.16746/) (2023)
- [Riemann2: Learning Riemannian Submanifolds from Riemannian Data](https://mlsanity.com/paper/2503.05540/) (2025)
- [Visualizing Riemannian data with Rie-SNE](https://mlsanity.com/paper/2203.09253/) (2022)

## Abstract (arXiv)

Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an ambient Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geometry might induce a suboptimal similarity measure, which could be improved by choosing a different metric. Euclidean models ignore such information and assign probability mass to data points that can never appear as data, and vastly different likelihoods to points that are similar under the desired metric. We propose the wrapped Gaussian process latent variable model (WGPLVM), that extends Gaussian process latent variable models to take values strictly on a given ambient Riemannian manifold, making the model blind to impossible data points. This allows non-linear, probabilistic inference of low-dimensional Riemannian submanifolds from data. Our evaluation on diverse datasets show that we improve performance on several tasks, including encoding, visualization and uncertainty quantification.