# Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifolds

arXiv: https://arxiv.org/abs/2210.01672 · HTML: https://mlsanity.com/paper/2210.01672/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 72 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 26 of 26)

- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [TEACH: Temporal Action Composition for 3D Humans](https://mlsanity.com/paper/2209.04066/) (2022)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Latent Variable Modelling with Hyperbolic Normalizing Flows](https://mlsanity.com/paper/2002.06336/) (2020)
- [Adversarial Parametric Pose Prior](https://mlsanity.com/paper/2112.04203/) (2021)
- [Computationally Tractable Riemannian Manifolds for Graph Embeddings](https://mlsanity.com/paper/2002.08665/) (2020)
- [Metrics for Probabilistic Geometries](https://mlsanity.com/paper/1411.7432/) (2014)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Heterogeneous manifolds for curvature-aware graph embedding](https://mlsanity.com/paper/2202.01185/) (2022)
- [Rethinking the compositionality of point clouds through regularization in the hyperbolic space](https://mlsanity.com/paper/2209.10318/) (2022)
- [Neural Distance Embeddings for Biological Sequences](https://mlsanity.com/paper/2109.09740/) (2021)
- [Manifold GPLVMs for discovering non-Euclidean latent structure in neural data](https://mlsanity.com/paper/2006.07429/) (2020)
- [A Motion Taxonomy for Manipulation Embedding](https://mlsanity.com/paper/2007.06695/) (2020)
- [Manipulation Motion Taxonomy and Coding for Robots](https://mlsanity.com/paper/1910.00532/) (2019)
- [Isometric Gaussian Process Latent Variable Model for Dissimilarity Data](https://mlsanity.com/paper/2006.11741/) (2020)

## Built on by (most cited first, 10 of 10)

- [Transfer Learning in Robotics: An Upcoming Breakthrough? A Review of Promises and Challenges](https://mlsanity.com/paper/2311.18044/) (2023)
- [The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphs](https://mlsanity.com/paper/2407.08086/) (2024)
- [Riemann2: Learning Riemannian Submanifolds from Riemannian Data](https://mlsanity.com/paper/2503.05540/) (2025)
- [Lemmanaid: Neuro-Symbolic Lemma Conjecturing](https://mlsanity.com/paper/2504.04942/) (2025)
- [Residual Deep Gaussian Processes on Manifolds](https://mlsanity.com/paper/2411.00161/) (2024)
- [On Probabilistic Pullback Metrics for Latent Hyperbolic Manifolds](https://mlsanity.com/paper/2410.20850/) (2024)
- [Randomized HyperSteiner: A Stochastic Delaunay Triangulation Heuristic for the Hyperbolic Steiner Minimal Tree](https://mlsanity.com/paper/2510.09328/) (2025)
- [Hyperboloid GPLVM for Discovering Continuous Hierarchies via Nonparametric Estimation](https://mlsanity.com/paper/2410.16698/) (2024)
- [Taxonomy-aware Dynamic Motion Generation on Hyperbolic Manifolds](https://mlsanity.com/paper/2509.21281/) (2025)
- [Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2610.03647/) (2026)

## Abstract (arXiv)

Human motion taxonomies serve as high-level hierarchical abstractions that classify how humans move and interact with their environment. They have proven useful to analyse grasps, manipulation skills, and whole-body support poses. Despite substantial efforts devoted to design their hierarchy and underlying categories, their use remains limited. This may be attributed to the lack of computational models that fill the gap between the discrete hierarchical structure of the taxonomy and the high-dimensional heterogeneous data associated to its categories. To overcome this problem, we propose to model taxonomy data via hyperbolic embeddings that capture the associated hierarchical structure. We achieve this by formulating a novel Gaussian process hyperbolic latent variable model that incorporates the taxonomy structure through graph-based priors on the latent space and distance-preserving back constraints. We validate our model on three different human motion taxonomies to learn hyperbolic embeddings that faithfully preserve the original graph structure. We show that our model properly encodes unseen data from existing or new taxonomy categories, and outperforms its Euclidean and VAE-based counterparts. Finally, through proof-of-concept experiments, we show that our model may be used to generate realistic trajectories between the learned embeddings.