# Minimum Density Hyperplanes

arXiv: https://arxiv.org/abs/1507.04201 · HTML: https://mlsanity.com/paper/1507.04201/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2015.

## Built on by (most cited first, 3 of 3)

- [Deep Clustering Using the Soft Silhouette Score: Towards Compact and Well-Separated Clusters](https://mlsanity.com/paper/2402.00608/) (2024)
- [HiPart: Hierarchical Divisive Clustering Toolbox](https://mlsanity.com/paper/2209.08680/) (2022)
- [Clustering Large Data Sets with Incremental Estimation of Low-density Separating Hyperplanes](https://mlsanity.com/paper/2108.03442/) (2021)

## Abstract (arXiv)

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark datasets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification.