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

• URL: http://arxiv.org/abs/2311.16614v4
• Date: Thu, 4 Jul 2024 17:51:38 GMT
• Title: A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections
• Authors: Prodromos Kolyvakis, Aristidis Likas,
• Abstract summary: We extend one-dimensional unimodality principles to multi-dimensional spaces through linear random projections and point-to-point distancing. Our method, rooted in $alpha$-unimodality assumptions, presents a novel unimodality test named mud-pod. Both theoretical and empirical studies confirm the efficacy of our method in unimodality assessment of multidimensional datasets.
• Score: 0.18416014644193066
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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