Home > Research > Publications & Outputs > Minimum Density Hyperplanes

Electronic data

  • Minimum_Density_Hyperplanes

    Accepted author manuscript, 3.29 MB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License


View graph of relations

Minimum Density Hyperplanes

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>28/09/2016
<mark>Journal</mark>Journal of Machine Learning Research
Issue number156
Number of pages33
Pages (from-to)1-33
Publication StatusPublished
<mark>Original language</mark>English


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 data sets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification.