A multi-variate blind source separation algorithm. (November 2017) - Goldhacker, M.; Keck, P.; Igel, A.; Lang, E.W.; Tomé, A.M.
Highlights: A multi-variate decomposition approach is presented, based on an approximate diagonalization of a set of matrices computed using a latent space representation. The proposed methodology follows an algebraic approach, which is common to space, temporal or spatio-temporal blind source separation algorithms. The resulting algorithms are applied to fMRI data sets, either to extract the underlying fMRI components or to resting state fMRI data collected for a dynamic functional connectivity analysis. Abstract: Background and objective: The study follows the proposal of decomposing a given data matrix into a product of independent spatial and temporal component matrices. A multi-variate decomposition approach is presented, based on an approximate diagonalization of a set of matrices computed using a latent space representation. Methods: The proposed methodology follows an algebraic approach, which is common to space, temporal or spatiotemporal blind source separation algorithms. More specifically, the algebraic approach relies on singular value decomposition techniques, which avoids computationally costly and numerically instable matrix inversion. The method is equally applicable to correlation matrices determined from second order correlations or by considering fourth order correlations. Results: The resulting algorithms are applied to fMRI data sets either to extract the underlying fMRI components or to extract connectivity maps from resting state fMRI data collected for a dynamic functional connectivity analysis. Intriguingly, our algorithm shows increased spatial specificity compared to common approaches, while temporal precision stays similar. Conclusion: The study presents a novel spatiotemporal blind source separation algorithm, which is both robust and avoids parameters that are difficult to fine tune. Applied on experimental data sets, the new method yields highly confined and focused areas with least spatial extent in the retinotopy case, and similar results in the dynamic functional connectivity analyses compared to other blind source separation algorithms. Therefore, we conclude that our novel algorithm is highly competitive and yields results, which are superior or at least similar to existing approaches.