# Accelerating hyperbolic t-SNE

arXiv: https://arxiv.org/abs/2401.13708 · HTML: https://mlsanity.com/paper/2401.13708/

## Key facts

- Cited by 3 papers in the map (data through 7 Oct 2026).
- Builds on 18 of its 65 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 18 of 18)

- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Differentiating through the Fr'echet Mean](https://mlsanity.com/paper/2003.00335/) (2020)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [Riemannian approach to batch normalization](https://mlsanity.com/paper/1709.09603/) (2017)
- [CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data](https://mlsanity.com/paper/2111.15037/) (2021)
- [Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Study](https://mlsanity.com/paper/2110.02894/) (2021)
- [Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning](https://mlsanity.com/paper/2305.18962/) (2023)
- [Hydra: A method for strain-minimizing hyperbolic embedding of network- and distance-based data](https://mlsanity.com/paper/1903.08977/) (2019)
- [VitaLITy: Promoting Serendipitous Discovery of Academic Literature with Transformers & Visual Analytics](https://mlsanity.com/paper/2108.03366/) (2021)
- [Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform](https://mlsanity.com/paper/2211.03635/) (2022)
- [Browser-based Hyperbolic Visualization of Graphs](https://mlsanity.com/paper/2205.08028/) (2022)
- [Limitations on Realistic Hyperbolic Graph Drawing](https://mlsanity.com/paper/2108.07441/) (2021)
- [Navigating Higher Dimensional Spaces using Hyperbolic Geometry](https://mlsanity.com/paper/2110.00327/) (2021)
- [PromotionLens: Inspecting Promotion Strategies of Online E-commerce via Visual Analytics](https://mlsanity.com/paper/2208.01404/) (2022)

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

- [ModalChorus: Visual Probing and Alignment of Multi-modal Embeddings via Modal Fusion Map](https://mlsanity.com/paper/2407.12315/) (2024)
- [Klein Model for Hyperbolic Neural Networks](https://mlsanity.com/paper/2410.16813/) (2024)
- [On the Abundance of Critical Points of the t-SNE Energy](https://mlsanity.com/paper/2609.04379/) (2026)

## Abstract (arXiv)

The need to understand the structure of hierarchical or high-dimensional data is present in a variety of fields. Hyperbolic spaces have proven to be an important tool for embedding computations and analysis tasks as their non-linear nature lends itself well to tree or graph data. Subsequently, they have also been used in the visualization of high-dimensional data, where they exhibit increased embedding performance. However, none of the existing dimensionality reduction methods for embedding into hyperbolic spaces scale well with the size of the input data. That is because the embeddings are computed via iterative optimization schemes and the computation cost of every iteration is quadratic in the size of the input. Furthermore, due to the non-linear nature of hyperbolic spaces, Euclidean acceleration structures cannot directly be translated to the hyperbolic setting. This paper introduces the first acceleration structure for hyperbolic embeddings, building upon a polar quadtree. We compare our approach with existing methods and demonstrate that it computes embeddings of similar quality in significantly less time. Implementation and scripts for the experiments can be found at https://graphics.tudelft.nl/accelerating-hyperbolic-tsne.