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

Prodromos Kolyvakis, Aristidis Likas
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:2255-2268, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v286-kolyvakis25a, 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}, pages = {2255--2268}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/kolyvakis25a/kolyvakis25a.pdf}, url = {https://proceedings.mlr.press/v286/kolyvakis25a.html}, 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.} }
Endnote
%0 Conference Paper %T A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections %A Prodromos Kolyvakis %A Aristidis Likas %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-kolyvakis25a %I PMLR %P 2255--2268 %U https://proceedings.mlr.press/v286/kolyvakis25a.html %V 286 %X 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.
APA
Kolyvakis, P. & Likas, A.. (2025). 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, in Proceedings of Machine Learning Research 286:2255-2268 Available from https://proceedings.mlr.press/v286/kolyvakis25a.html.

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