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Unimodality, pivotal in statistical analysis, offers insights into datasetstructures and drives sophisticated analytical procedures. While unimodality'sconfirmation is straightforward for one-dimensional data using methods likeSilverman's approach and Hartigans' dip statistic, its generalization to higherdimensions remains challenging. By extrapolating one-dimensional unimodalityprinciples to multi-dimensional spaces through linear random projections andleveraging point-to-point distancing, our method, rooted in$\alpha$-unimodality assumptions, presents a novel multivariate unimodalitytest named mud-pod. Both theoretical and empirical studies confirm the efficacyof our method in unimodality assessment of multidimensional datasets as well asin estimating the number of clusters.

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