Guarantees for Hierarchical Clustering by the Sublevel Set method

TL;DR

This paper extends the Sublevel Set method to hierarchical clustering, providing guarantees of near-optimality and correctness without distribution assumptions, enhancing theoretical understanding of clustering methods.

Contribution

It adapts the Sublevel Set method to Dasgupta's hierarchical clustering framework, offering new theoretical guarantees.

Findings

Provides theoretical guarantees for hierarchical clustering

Extends the Sublevel Set method to new clustering paradigms

Enhances understanding of clustering optimality

Abstract

Meila (2018) introduces an optimization based method called the Sublevel Set method, to guarantee that a clustering is nearly optimal and "approximately correct" without relying on any assumptions about the distribution that generated the data. This paper extends the Sublevel Set method to the cost-based hierarchical clustering paradigm proposed by Dasgupta (2016).