Generalised Bayesian matrix factorisation models

Factor analysis and related models for probabilistic matrix factorisation are of central importance to the unsupervised analysis of data, with a colourful history more than a century long. Probabilistic models for matrix factorisation allow us to explore the underlying structure in data, and have relevance in a vast number of application areas including collaborative filtering, source separation, missing data imputation, gene expression analysis, information retrieval, computational finance and computer vision, amongst others. This thesis develops generalisations of matrix factorisation models that advance our understanding and enhance the applicability of this important class of models. The generalisation of models for matrix factorisation focuses on three concerns: widening the applicability of latent variable models to the diverse types of data that are currently available; considering alternative structural forms in the underlying representations that are inferred; and including higher order data structures into the matrix factorisation framework. These three issues reflect the reality of modern data analysis and we develop new models that allow for a principled exploration and use of data in these settings. We place emphasis on Bayesian approaches to learning and the advantages that come with the Bayesian methodology. Our port of departure is a generalisation of latent variable models to members of the exponential family of distributions. This generalisation allows for the analysis of data that may be real-valued, binary, counts, non-negative or a heterogeneous set of these data types. The model unifies various existing models and constructs for unsupervised settings, the complementary framework to the generalised linear models in regression. Moving to structural considerations, we develop Bayesian methods for learning sparse latent representations. We define ideas of weakly and strongly sparse vectors and investigate the classes of prior distributions that give rise to these forms of sparsity, namely the scale-mixture of Gaussians and the spike-and-slab distribution. Based on these sparsity favouring priors, we develop and compare methods for sparse matrix factorisation and present the first comparison of these sparse learning approaches. As a second structural consideration, we develop models with the ability to generate correlated binary vectors. Moment-matching is used to allow binary data with specified correlation to be generated, based on dichotomisation of the Gaussian distribution. We then develop a novel and simple method for binary PCA based on Gaussian dichotomisation. The third generalisation considers the extension of matrix factorisation models to multi-dimensional arrays of data that are increasingly prevalent. We develop the first Bayesian model for non-negative tensor factorisation and explore the relationship between this model and the previously described models for matrix factorisation.Supported by a Commonwealth Scholarship awarded by the Commonwealth Scholarship and Fellowship Programme (CSFP) [Award number ZACS-2207-363] Supported by award from the National Research Foundation, South Africa (NRF) [Award number SFH2007072200001

Development of a Handheld Scanning Transducer Probe for Ultrasound Imaging

The scanning transducer technique is a simple and cost effective approach to achieve ultrasound imaging. By mechanically scanning a single-element transducer with a motor stage, the time-variant ultrasound field at an array of locations can be recorded for image reconstruction. When compared with the use of conventional transducer arrays, the scanning transducer approach requires much less data acquisition electronics. However, conventional x-y motor stages used for scanning the transducer are complex, bulky and slow. As a result, the scanning transducer technique for image acquisition has been mainly limited for lab use and is not suitable for handheld imaging applications. The goal of this research is to achieve a new 2-axis scanning transducer probe for handheld ultrasound imaging operations, which is compact and light-weight. The approach is to develop and capitalize upon a miniaturized water-immersible 2-axis electromagnetic actuator to enable fast and agile scanning of a single-element transducer in a liquid filled probe case. The design and fabrication of a water-immersible 2-axis electromagnetic actuator has been achieved and its mechanical scanning performance has been characterized and optimized with finite-element simulation. Preliminary pulse-echo imaging experiments were performed to verify its ultrasound imaging capability with scanning in B-scan mode in multiple directions. The scan system built can be dynamically reconfigured to either 1D- B-Scan or even 2D C-Scan formats for conventional 2D as well as 3D ultrasound imaging. In addition, integrated optical light delivery with optic fiber cables was also investigated to extend its capability for photoacoustic imaging