# nSimplex Zen: A Novel Dimensionality Reduction for Euclidean and Hilbert Spaces

arXiv: https://arxiv.org/abs/2302.11508 · HTML: https://mlsanity.com/paper/2302.11508/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 65 references that are in the map.
- First posted on arXiv 22 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [YFCC100M: The New Data in Multimedia Research](https://mlsanity.com/paper/1503.01817/) (2015)
- [Experiments with Random Projection](https://mlsanity.com/paper/1301.3849/) (2013)
- [Hardness of Approximate Nearest Neighbor Search](https://mlsanity.com/paper/1803.00904/) (2018)
- [High-Dimensional Simplexes for Supermetric Search](https://mlsanity.com/paper/1707.08370/) (2017)
- [Hilbert Exclusion: Improved Metric Search through Finite Isometric Embeddings](https://mlsanity.com/paper/1604.08640/) (2016)
- [Supermetric Search](https://mlsanity.com/paper/1707.08361/) (2017)

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

- ["Normalized Stress" is Not Normalized: How to Interpret Stress Correctly](https://mlsanity.com/paper/2408.07724/) (2024)
- [How Scale Breaks "Normalized Stress" and KL Divergence: Rethinking Quality Metrics](https://mlsanity.com/paper/2510.08660/) (2025)
- [Ultra-Quantisation: Efficient Embedding Search via 1.58-bit Encodings](https://mlsanity.com/paper/2506.00528/) (2025)

## Abstract (arXiv)

Dimensionality reduction techniques map values from a high dimensional space to one with a lower dimension. The result is a space which requires less physical memory and has a faster distance calculation. These techniques are widely used where required properties of the reduced-dimension space give an acceptable accuracy with respect to the original space. Many such transforms have been described. They have been classified in two main groups: linear and topological. Linear methods such as Principal Component Analysis (PCA) and Random Projection (RP) define matrix-based transforms into a lower dimension of Euclidean space. Topological methods such as Multidimensional Scaling (MDS) attempt to preserve higher-level aspects such as the nearest-neighbour relation, and some may be applied to non-Euclidean spaces. Here, we introduce nSimplex Zen, a novel topological method of reducing dimensionality. Like MDS, it relies only upon pairwise distances measured in the original space. The use of distances, rather than coordinates, allows the technique to be applied to both Euclidean and other Hilbert spaces, including those governed by Cosine, Jensen-Shannon and Quadratic Form distances. We show that in almost all cases, due to geometric properties of high-dimensional spaces, our new technique gives better properties than others, especially with reduction to very low dimensions.