# Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations

arXiv: https://arxiv.org/abs/1902.05804 · HTML: https://mlsanity.com/paper/1902.05804/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2019.

## Built on by (most cited first, 22 of 22)

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- [May the force be with you](https://mlsanity.com/paper/2208.06676/) (2022)
- [Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels](https://mlsanity.com/paper/2505.24311/) (2025)
- [FUnc-SNE: A flexible, Fast, and Unconstrained algorithm for neighbour embeddings](https://mlsanity.com/paper/2509.07681/) (2025)
- [The Tree-SNE Tree Exists](https://mlsanity.com/paper/2510.15014/) (2025)
- [How smoothing the affinity matrix affects neighborhood preservation in t-SNE](https://mlsanity.com/paper/2608.17190/) (2026)

## Abstract (arXiv)

T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient implementation of t-SNE for a t-distribution kernel with an arbitrary degree of freedom nu, with nu→∞ corresponding to SNE and nu=1 corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that nu<1 can further reduce the crowding problem and reveal finer cluster structure that is invisible in standard t-SNE. We further demonstrate the striking effect of heavier-tailed kernels on large real-life data sets such as MNIST, single-cell RNA-sequencing data, and the HathiTrust library. We use domain knowledge to confirm that the revealed clusters are meaningful. Overall, we argue that modifying the tail heaviness of the t-SNE kernel can yield additional insight into the cluster structure of the data.