A Multivariate Unimodality Test Harnessing the Dip Statistic of Mahalanobis Distances Over Random Projections
This provides a solution for statisticians and data analysts needing to analyze high-dimensional data structures, though it appears incremental by extending one-dimensional principles.
The paper tackles the challenge of testing unimodality in multivariate data by introducing mud-pod, a method based on random projections and Mahalanobis distances, which effectively assesses unimodality and estimates cluster numbers in multidimensional datasets.
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 $α$-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.