# Non-Euclidean Self-Organizing Maps

arXiv: https://arxiv.org/abs/2109.11769 · HTML: https://mlsanity.com/paper/2109.11769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 45 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?](https://mlsanity.com/paper/1407.0611/) (2014)
- [Ray-marching Thurston geometries](https://mlsanity.com/paper/2010.15801/) (2020)

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

- [Neuro-mimetic Task-free Unsupervised Online Learning with Continual Self-Organizing Maps](https://mlsanity.com/paper/2402.12465/) (2024)

## Abstract (arXiv)

Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs. Most data analysts take it for granted to use some subregions of a flat space as their data model; however, by the assumption that the underlying geometry is non-Euclidean we obtain a new degree of freedom for the techniques that translate the similarities into spatial neighborhood relationships. We improve the traditional SOM algorithm by introducing topology-related extensions. Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data (both hierarchical and non-hierarchical).