Statistical analysis of a hierarchical clustering algorithm with outliers

TL;DR

This paper introduces a new hierarchical clustering algorithm designed to effectively identify clusters despite the presence of outliers, backed by theoretical guarantees and empirical validation.

Contribution

A novel hierarchical clustering method with proven robustness to outliers, including theoretical performance bounds and empirical comparisons.

Findings

Algorithm recovers true clusters with high probability

Establishes consistency and convergence rates

Outperforms classical methods in simulations

Abstract

It is well known that the classical single linkage algorithm usually fails to identify clusters in the presence of outliers. In this paper, we propose a new version of this algorithm, and we study its mathematical performances. In particular, we establish an oracle type inequality which ensures that our procedure allows to recover the clusters with large probability under minimal assumptions on the distribution of the outliers. We deduce from this inequality the consistency and some rates of convergence of our algorithm for various situations. Performances of our approach is also assessed through simulation studies and a comparison with classical clustering algorithms on simulated data is also presented.