A parallelizable model-based approach for marginal and multivariate clustering

TL;DR

This paper introduces a parallelizable, margin-specific mixture model clustering method called Reign-and-Conquer, which allows different numbers of clusters per margin and is computationally efficient for high-dimensional data.

Contribution

It proposes a novel, parallelizable clustering approach that relaxes the assumption of equal clusters across margins by specifying separate mixture models per margin.

Findings

Good performance on artificial datasets across scenarios

Effective application on real datasets

More computationally tractable than full joint models

Abstract

This paper develops a clustering method that takes advantage of the sturdiness of model-based clustering, while attempting to mitigate some of its pitfalls. First, we note that standard model-based clustering likely leads to the same number of clusters per margin, which seems a rather artificial assumption for a variety of datasets. We tackle this issue by specifying a finite mixture model per margin that allows each margin to have a different number of clusters, and then cluster the multivariate data using a strategy game-inspired algorithm to which we call Reign-and-Conquer. Second, since the proposed clustering approach only specifies a model for the margins -- but leaves the joint unspecified -- it has the advantage of being partially parallelizable; hence, the proposed approach is computationally appealing as well as more tractable for moderate to high dimensions than a `full' (joint) model-based clustering approach. A battery of numerical experiments on artificial data indicate an overall good performance of the proposed methods in a variety of scenarios, and real datasets are used to showcase their application in practice.