# Navigating Perplexity: A linear relationship with the data set size in t-SNE embeddings

arXiv: https://arxiv.org/abs/2308.15513 · HTML: https://mlsanity.com/paper/2308.15513/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
- [Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Study](https://mlsanity.com/paper/2110.02894/) (2021)
- [Approximated and User Steerable tSNE for Progressive Visual Analytics](https://mlsanity.com/paper/1512.01655/) (2015)
- [Automatic Selection of t-SNE Perplexity](https://mlsanity.com/paper/1708.03229/) (2017)
- [Perplexity-free Parametric t-SNE](https://mlsanity.com/paper/2010.01359/) (2020)

## Built on by (most cited first, 1 of 1)

- [Calibrating dimension reduction hyperparameters in the presence of noise](https://mlsanity.com/paper/2312.02946/) (2023)

## Abstract (arXiv)

Widely used pipelines for analyzing high-dimensional data utilize two-dimensional visualizations. These are created, for instance, via t-distributed stochastic neighbor embedding (t-SNE). A crucial element of the t-SNE embedding procedure is the perplexity hyperparameter. That is because the embedding structure varies when perplexity is changed. A suitable perplexity choice depends on the data set and the intended usage for the embedding. Therefore, perplexity is often chosen based on heuristics, intuition, and prior experience. This paper uncovers a linear relationship between perplexity and the data set size. Namely, we show that embeddings remain structurally consistent across data set samples when perplexity is adjusted accordingly. Qualitative and quantitative experimental results support these findings. This informs the visualization process, guiding the user when choosing a perplexity value. Finally, we outline several applications for the visualization of high-dimensional data via t-SNE based on this linear relationship.