# Geometric reconstructions of density based clusterings

arXiv: https://arxiv.org/abs/2203.08020 · HTML: https://mlsanity.com/paper/2203.08020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 14 Mar 2022.

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

- [Accelerated Hierarchical Density Clustering](https://mlsanity.com/paper/1705.07321/) (2017)
- [Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering](https://mlsanity.com/paper/2104.01126/) (2021)
- [Efficient Computation of Multiple Density-Based Clustering Hierarchies](https://mlsanity.com/paper/1709.04545/) (2017)

## Abstract (arXiv)

DBSCAN* and HDBSCAN* are well established density based clustering algorithms. However, obtaining the clusters of very large datasets is infeasible, limiting their use in real world applications. By exploiting the geometry of Euclidean space, we prove that it is possible to systematically construct the DBSCAN* and HDBSCAN* clusters of a finite Xsubset ℝn from specific subsets of X. We are able to control the size of these subsets and therefore our results make it possible to cluster very large datasets. To illustrate our theory, we cluster the Microsoft Building Footprint Database of the US, which is not possible using the standard implementations.