TY - JOUR

T1 - Minimum Density Hyperplanes

AU - Pavlidis, Nicos Georgios

AU - Hofmeyr, David

AU - Tasoulis, Sotiris

PY - 2016/9/28

Y1 - 2016/9/28

N2 - Associating distinct groups of objects (clusters) with contiguous regions ofhigh 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.

AB - Associating distinct groups of objects (clusters) with contiguous regions ofhigh 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.

KW - clustering

KW - semi-supervised classification

KW - projection pursuit

KW - low-density separation

KW - high-density clusters

M3 - Journal article

VL - 17

SP - 1

EP - 33

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

SN - 1532-4435

IS - 156

ER -