Exploring the latent space between brain and behaviour using eigen-decomposition methods

Machine learning methods have been successfully used to analyse neuroimaging data for a variety of applications, including the classification of subjects with different brain disorders. However, most studies still rely on the labelling of the subjects, constraining the study of several brain diseases within a paradigm of pre-defined clinical labels, which have shown to be unreliable in some cases. The lack of understanding regarding the association between brain and behaviour presents itself as an interesting challenge for more exploratory machine learning approaches, which could potentially help in the study of diseases whose clinical labels have shown limitations. The aim of this project is to explore the possibility of using eigen-decomposition approaches to find multivariate associative effects between brain structure and behaviour in an exploratory way. This thesis addresses a number of issues associated with eigen-decomposition methods, in order to enable their application to investigate brain/behaviour relationships in a reliable way. The first contribution was showing the advantages of an alternative matrix deflation approach to be used with Sparse Partial Least Squares (SPLS). The modified SPLS method was later used to model the associations between clinical/demographic data and brain structure, without relying on a priori assumptions on the sparsity of each data source. A novel multiple hold-out SPLS framework was then proposed, which allowed for the detection of robust multivariate associative effects between brain structure and individual questionnaire items. The linearity assumption of most machine learning methods used in neuroimaging might be a limitation, since these methods will not have enough flexibility to detect non-linear associations. In order to address this issue, a novel Sparse Canonical Correlation Analysis (SCCA) method was proposed, which allows one to use sparsity constraints in one data source (e.g. neuroimaging data), with non-linear transformations of the data in the other source (e.g. clinical data).