# Guaranteed Recovery of Unambiguous Clusters

arXiv: https://arxiv.org/abs/2501.13093 · HTML: https://mlsanity.com/paper/2501.13093/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 22 Jan 2025.

## Builds on (most cited first, 4 of 4)

- [DBSCAN++: Towards fast and scalable density clustering](https://mlsanity.com/paper/1810.13105/) (2018)
- [Density Level Set Estimation on Manifolds with DBSCAN](https://mlsanity.com/paper/1703.03503/) (2017)
- [The SpectACl of Nonconvex Clustering: A Spectral Approach to Density-Based Clustering](https://mlsanity.com/paper/1907.00680/) (2019)
- [AMD-DBSCAN: An Adaptive Multi-density DBSCAN for datasets of extremely variable density](https://mlsanity.com/paper/2210.08162/) (2022)

## Abstract (arXiv)

Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters K is known, this ambiguity often still exists, particularly when there is variation in density among different clusters, and clusters have multiple relatively separated regions of high density. In this paper we propose an information-theoretic characterization of when a K-clustering is ambiguous, and design an algorithm that recovers the clustering whenever it is unambiguous. This characterization formalizes the situation when two high density regions within a cluster are separable enough that they look more like two distinct clusters than two truly distinct clusters in the K-clustering. The algorithm first identifies K partial clusters (or "seeds") using a density-based approach, and then adds unclustered points to the initial K partial clusters in a greedy manner to form a complete clustering. We implement and test a version of the algorithm that is modified to effectively handle overlapping clusters, and observe that it requires little parameter selection and displays improved performance on many datasets compared to widely used algorithms for non-convex cluster recovery.