Persistent Multiscale Density-based Clustering

TL;DR

This paper introduces PLSCAN, a new density-based clustering algorithm that identifies stable clusters across scales, reducing hyperparameter sensitivity and improving robustness in exploratory data analysis.

Contribution

The paper presents PLSCAN, a novel scale-space clustering method based on persistent homology, which efficiently finds stable clusters without extensive hyperparameter tuning.

Findings

PLSCAN outperforms HDBSCAN* in clustering accuracy (higher ARI).

PLSCAN is less sensitive to the number of neighbors.

It has competitive computational costs, especially in low dimensions.

Abstract

Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN). This novel density-based clustering algorithm efficiently identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher average ARI and is less sensitive to changes in the number of mutual reachability neighbours. Additionally, we compare PLSCAN's computational costs to k-Means, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.