# MNIST-Nd: a set of naturalistic datasets to benchmark clustering across dimensions

arXiv: https://arxiv.org/abs/2410.16124 · HTML: https://mlsanity.com/paper/2410.16124/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 21 Oct 2024.

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

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [A framework for benchmarking clustering algorithms](https://mlsanity.com/paper/2209.09493/) (2022)
- [Minimum adjusted Rand index for two clusterings of a given size](https://mlsanity.com/paper/2002.03677/) (2020)
- [DCSI -- An improved measure of cluster separability based on separation and connectedness](https://mlsanity.com/paper/2310.12806/) (2023)

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

- [Hierarchical clustering with maximum density paths and mixture models](https://mlsanity.com/paper/2503.15582/) (2025)

## Abstract (arXiv)

Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for instance to understand the organization of different cell types. However, clustering is known to scale poorly to high dimensions, even though the exact impact of dimensionality is unclear as current benchmark datasets are mostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets that share a key property of real-world datasets, namely that individual samples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained by training mixture variational autoencoders with 2 to 64 latent dimensions on MNIST, resulting in six datasets with comparable structure but varying dimensionality. It thus offers the chance to disentangle the impact of dimensionality on clustering. Preliminary common clustering algorithm benchmarks on MNIST-Nd suggest that Leiden is the most robust for growing dimensions.