The Why and How of Convex Clustering

TL;DR

This survey explains convex clustering, a stable, globally optimal, and tunable clustering method based on convex optimization, highlighting its theoretical properties, algorithms, and practical applications.

Contribution

It provides a comprehensive overview of convex clustering, emphasizing its unique features, theoretical stability, and practical algorithms, which distinguish it from other clustering methods.

Findings

Convex clustering has a unique global minimum free of spurious local minima.

Its single tuning parameter effectively controls the number of clusters.

The method is flexible and can be integrated with other inferential techniques.

Abstract

This survey reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from prior art. The optimization problem is free of spurious local minima, and its unique global minimizer is stable with respect to all its inputs, including the data, a tuning parameter, and weight hyperparameters. Its single tuning parameter controls the number of clusters and can be chosen using standard techniques from penalized regression. We give intuition into the behavior and theory for convex clustering as well as practical guidance. We highlight important algorithms and discuss how their computational costs scale with the problem size. Finally, we highlight the breadth of its uses and flexibility to be combined and integrated with other inferential methods.