A density-sensitive hierarchical clustering method

TL;DR

This paper introduces a density-sensitive hierarchical clustering method called $SL(eta)$ that addresses the chaining effect by considering data density, with theoretical analysis and a modified version to handle chaining through points or small blocks.

Contribution

The paper proposes a new density-sensitive hierarchical clustering algorithm and its variant, providing theoretical insights into their properties and effectiveness against chaining effects.

Findings

The methods are sensitive to data density and mitigate chaining effects.

Theoretical properties of the algorithms are established.

A modified version improves chaining through points or small blocks.

Abstract

We define a hierarchical clustering method: $\alpha$-unchaining single linkage or $SL(\alpha)$. The input of this algorithm is a finite metric space and a certain parameter $\alpha$. This method is sensitive to the density of the distribution and offers some solution to the so called chaining effect. We also define a modified version, $SL^*(\alpha)$, to treat the chaining through points or small blocks. We study the theoretical properties of these methods and offer some theoretical background for the treatment of chaining effects.