# SQuadMDS: a lean Stochastic Quartet MDS improving global structure preservation in neighbor embedding like t-SNE and UMAP

arXiv: https://arxiv.org/abs/2202.12087 · HTML: https://mlsanity.com/paper/2202.12087/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 44 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 2 of 2)

- [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)

## Built on by (most cited first, 5 of 5)

- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction](https://mlsanity.com/paper/2508.13747/) (2025)
- [VERA: Generating Visual Explanations of Two-Dimensional Embeddings via Region Annotation](https://mlsanity.com/paper/2406.04808/) (2024)
- [FloDR: An invertible dimensionality reduction method based on a normalising flow](https://mlsanity.com/paper/2607.26278/) (2026)
- [FUnc-SNE: A flexible, Fast, and Unconstrained algorithm for neighbour embeddings](https://mlsanity.com/paper/2509.07681/) (2025)

## Abstract (arXiv)

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to have high computational complexities, making them inapplicable on large data sets. This work introduces a stochastic, force directed approach to multidimensional scaling with a time and space complexity of O(N), with N data points. The method can be combined with force directed layouts of the family of neighbour embedding such as t-SNE, to produce embeddings that preserve both the global and the local structures of the data. Experiments assess the quality of the embeddings produced by the standalone version and its hybrid extension both quantitatively and qualitatively, showing competitive results outperforming state-of-the-art approaches. Codes are available at https://github.com/PierreLambert3/SQuaD-MDS-and-FItSNE-hybrid.