  In this study we adopt predictive modelling to identify simultaneously
commonalities and differences in multi-modal brain networks acquired within
subjects. Typically, predictive modelling of functional connectomes from
structural connectomes explores commonalities across multimodal imaging data.
However, direct application of multivariate approaches such as sparse Canonical
Correlation Analysis (sCCA) applies on the vectorised elements of functional
connectivity across subjects and it does not guarantee that the predicted
models of functional connectivity are Symmetric Positive Matrices (SPD). We
suggest an elegant solution based on the transportation of the connectivity
matrices on a Riemannian manifold, which notably improves the prediction
performance of the model. Randomised lasso is used to alleviate the dependency
of the sCCA on the lasso parameters and control the false positive rate.
Subsequently, the binomial distribution is exploited to set a threshold
statistic that reflects whether a connection is selected or rejected by chance.
Finally, we estimate the sCCA loadings based on a de-noising approach that
improves the estimation of the coefficients. We validate our approach based on
resting-state fMRI and diffusion weighted MRI data. Quantitative validation of
the prediction performance shows superior performance, whereas qualitative
results of the identification process are promising.
