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

arXiv: https://arxiv.org/abs/2311.16614 · HTML: https://mlsanity.com/paper/2311.16614/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Stop using the elbow criterion for k-means and how to choose the number of clusters instead](https://mlsanity.com/paper/2212.12189/) (2022)
- [RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections](https://mlsanity.com/paper/1405.1792/) (2014)
- [The UU-test for Statistical Modeling of Unimodal Data](https://mlsanity.com/paper/2008.12537/) (2020)
- [Universal Inference Meets Random Projections: A Scalable Test for Log-concavity](https://mlsanity.com/paper/2111.09254/) (2021)

## Built on by (most cited first, 2 of 2)

- [UniForCE: The Unimodality Forest Method for Clustering and Estimation of the Number of Clusters](https://mlsanity.com/paper/2312.11323/) (2023)
- [Hierarchical clustering with maximum density paths and mixture models](https://mlsanity.com/paper/2503.15582/) (2025)

## Abstract (arXiv)

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.