This thesis details theoretical and empirical work that draws from two main subject areas: Machine
Learning (ML) and Digital Signal Processing (DSP). A unified general framework is given for the application
of sparse machine learning methods to multivariate signal processing. In particular, methods that
enforce sparsity will be employed for reasons of computational efficiency, regularisation, and compressibility.
The methods presented can be seen as modular building blocks that can be applied to a variety
of applications. Application specific prior knowledge can be used in various ways, resulting in a flexible
and powerful set of tools. The motivation for the methods is to be able to learn and generalise from a set
of multivariate signals.
In addition to testing on benchmark datasets, a series of empirical evaluations on real world
datasets were carried out. These included: the classification of musical genre from polyphonic audio
files; a study of how the sampling rate in a digital radar can be reduced through the use of Compressed
Sensing (CS); analysis of human perception of different modulations of musical key from
Electroencephalography (EEG) recordings; classification of genre of musical pieces to which a listener
is attending from Magnetoencephalography (MEG) brain recordings. These applications demonstrate
the efficacy of the framework and highlight interesting directions of future research
