A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances over Random Projections
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.
Cite
Text
Kolyvakis and Likas. "A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances over Random Projections." Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, 2025.Markdown
[Kolyvakis and Likas. "A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances over Random Projections." Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, 2025.](https://mlanthology.org/uai/2025/kolyvakis2025uai-multivariate/)BibTeX
@inproceedings{kolyvakis2025uai-multivariate,
title = {{A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances over Random Projections}},
author = {Kolyvakis, Prodromos and Likas, Aristidis},
booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence},
year = {2025},
pages = {2255-2268},
volume = {286},
url = {https://mlanthology.org/uai/2025/kolyvakis2025uai-multivariate/}
}