A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections

Prodromos Kolyvakis, Aristidis Likas

Keywords: multivariate unimodality test, alpha-unimodality, dip test, random projections, clustering, cluster number estimation

Abstract:

Unimodality, pivotal in statistical analysis, offers insights into dataset structures and drives sophisticated analytical procedures.
While unimodality's confirmation is straightforward for one-dimensional data using methods like Silverman's approach and Hartigans' dip statistic, its generalization to higher dimensions remains challenging.
By extrapolating one-dimensional unimodality principles to multi-dimensional spaces through linear random projections and leveraging point-to-point distancing, our method, rooted in $\alpha$-unimodality assumptions, presents a novel multivariate unimodality test named $\textit{mud-pod}$.
Both theoretical and empirical studies confirm the efficacy of our method in unimodality assessment of multidimensional datasets as well as in estimating the number of clusters.

Code Link: https://github.com/prokolyvakis/mudpod

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission275/Authors, auai.org/UAI/2025/Conference/Submission275/Reproducibility_Reviewers

Submission Number: 275