Quantile-based clustering

TL;DR

The paper introduces $K$-quantiles clustering, a flexible, scalable nonparametric method that handles skewness and high-dimensional data, with proven consistency and competitive performance in simulations and real datasets.

Contribution

It presents a novel $K$-quantiles clustering algorithm that is simple, efficient, and adaptable to skewed and high-dimensional data, with theoretical guarantees.

Findings

Proven consistency of $K$-quantiles clustering.

Comparable or superior performance in simulations.

Effective application to high-dimensional microarray data.

Abstract

A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and high-dimensional datasets. It allows for within-cluster skewness and internal variable scaling based on within-cluster variation. Different versions allow for different levels of parsimony and computational efficiency. Although $K$-quantiles clustering is conceived as nonparametric, it can be connected to a fixed partition model of generalized asymmetric Laplace-distributions. The consistency of $K$-quantiles clustering is proved, and it is shown that $K$-quantiles clusters correspond to well separated mixture components in a nonparametric mixture. In a simulation, $K$-quantiles clustering is compared with a number of popular clustering methods with good results. A high-dimensional microarray dataset is clustered by $K$-quantiles.