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

## TL;DR

SpectACl is a novel spectral clustering method that combines minimum cut and density-based paradigms to effectively handle nonconvex shapes, noise, and varying densities, providing robust results.

## Contribution

It introduces SpectACl, a new spectral clustering approach that integrates density criteria to overcome limitations of existing methods.

## Key findings

- SpectACl outperforms traditional methods on synthetic data.
- It demonstrates robustness to noise and density variations.
- The method is easy to implement and theoretically grounded.

## Abstract

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 \textsc{SpectACl}: 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.