Unsupervised Classification of Functions using Dirichlet Process Mixtures of Gaussian Processes

This technical report presents a novel algorithm for unsupervised clustering of functions. It proceeds by developing the theory of unsupervised classification in mixtures from the familiar mixture of Gaussian distributions, to the infinite mixture of Gaussian processes. At each stage a both a theoretical and an algorithmic exposition are presented. We consider unsupervised classification (or clustering) of functions where the functions are not limited to parametric forms and the number of function clusters is initially unknown. We approach this problem by considering an hierarchical model in which the functions are realisations from an infinite mixture of Gaussian processes, which is drawn from a Dirichlet process mixture. The primary difficulty in this approach is sampling the latent variables associating functions with their cognate Gaussian process, as this amounts to sampling from an infinite mixture. We show this may be achieved using the technique of retrospective sampling. Finally we present empirical data using both a synthetic problem and cell-cycle mRNA expression time-course data.