Topics in unsupervised learning

Abstract

Two topics in unsupervised learning are reviewed and developed; namely, model-based clustering and association rule mining. A new family of Gaussian mixture models, with a parsim onious covariance structure, is introduced. The mixtures of factor analysers and mixtures of principal component analysers models are special cases of this new family of models. This family exhibit the feature that their number of covariance parameters grows linearly with the dimensionality of the data, which leads to relatively fast computation time. These models perform excellently, compared to popular model-based clustering techniques, when applied to real data. A new family of Gaussian mixture models with a Cholesky-decomposed covariance structure is also introduced. Four members of this family are developed and applied to real data. This family of models has great potential for further development in future work. A novel approach, via association rules, is taken to the analysis of college applications data. This analysis contributes to the discussion about the existence of a 'points race'. A new method of quantifying and visualising the interestingness of an association rule is also introduced and an argument for the inclusion of negations in the association rule mining process is given.