# The SpectACl of Nonconvex Clustering: A Spectral Approach to Density-Based Clustering

arXiv: https://arxiv.org/abs/1907.00680 · HTML: https://mlsanity.com/paper/1907.00680/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [Enhancing cluster analysis via topological manifold learning](https://mlsanity.com/paper/2207.00510/) (2022)
- [Git: Clustering Based on Graph of Intensity Topology](https://mlsanity.com/paper/2110.01274/) (2021)
- [visClust: A visual clustering algorithm based on orthogonal projections](https://mlsanity.com/paper/2211.03894/) (2022)
- [Guaranteed Recovery of Unambiguous Clusters](https://mlsanity.com/paper/2501.13093/) (2025)
- [Scalable Varied-Density Clustering via Graph Propagation](https://mlsanity.com/paper/2508.02989/) (2025)
- [Towards Robust and Scalable Density-based Clustering via Graph Propagation](https://mlsanity.com/paper/2605.00390/) (2026)

## Abstract (arXiv)

When it comes to clustering nonconvex shapes, two paradigms are used to find the most suitable clustering: minimum cut and maximum density. The most popular algorithms incorporating these paradigms are Spectral Clustering and DBSCAN. Both paradigms have their pros and cons. While minimum cut clusterings are sensitive to noise, density-based clusterings have trouble handling clusters with varying densities. In this paper, we propose textscSpectACl: a method combining the advantages of both approaches, while solving the two mentioned drawbacks. Our method is easy to implement, such as spectral clustering, and theoretically founded to optimize a proposed density criterion of clusterings. Through experiments on synthetic and real-world data, we demonstrate that our approach provides robust and reliable clusterings.