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.

通过线性随机投影和点对点距离计算，我们提出了一种根据 α- 单峰假设的多元单峰性测试方法，命名为 mud-pod，通过将一维单峰性原理推广到多维空间中，从而在多维数据集的单峰性评估和聚类数量估计方面表现出良好效果。