Browsing by Author "Hofmeyr, David P."

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    Minimum density hyperplanes
    (Journal of Machine Learning Research, 2016) Pavlidis, Nicos G.; Hofmeyr, David P.; Tasoulis, Sotiris K.
    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.
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    PPCI : an R package for cluster identification using projection pursuit
    (Projection pursuit (Statistics) -- Methods, 2019-12) Hofmeyr, David P.; Pavlidis, Nicos G.
    This paper presents the R package PPCI which implements three recently proposed projection pursuit methods for clustering. The methods are unified by the approach of defining an optimal hyperplane to separate clusters, and deriving a projection index whose optimiser is the vector normal to this separating hyperplane. Divisive hierarchical clustering algorithms that can detect clusters defined in different subspaces are readily obtained by recursively bi-partitioning the data through such hyperplanes. Projecting onto the vector normal to the optimal hyperplane enables visualisations of the data that can be used to validate the partition at each level of the cluster hierarchy. Clustering models can also be modified in an interactive manner to improve their solutions. Extensions to problems involving clusters which are not linearly separable, and to the problem of finding maximum hard margin hyperplanes for clustering are also discussed.