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arXiv · 2110.13502

Shared Independent Component Analysis for Multi-Subject Neuroimaging

Hugo Richard·Pierre Ablin·Bertrand Thirion·Alexandre Gramfort·Aapo Hyvärinen
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Abstract

We consider shared response modeling, a multi-view learning problem where one wants to identify common components from multiple datasets or views. We introduce Shared Independent Component Analysis (ShICA) that models each view as a linear transform of shared independent components contaminated by additive Gaussian noise. We show that this model is identifiable if the components are either non-Gaussian or have enough diversity in noise variances. We then show that in some cases multi-set canonical correlation analysis can recover the correct unmixing matrices, but that even a small amount of sampling noise makes Multiset CCA fail. To solve this problem, we propose to use joint diagonalization after Multiset CCA, leading to a new approach called ShICA-J. We show via simulations that ShICA-J leads to improved results while being very fast to fit. While ShICA-J is based on second-order statistics, we further propose to leverage non-Gaussianity of the components using a maximum-likelihood method, ShICA-ML, that is both more accurate and more costly. Further, ShICA comes with a principled method for shared components estimation. Finally, we provide empirical evidence on fMRI and MEG datasets that ShICA yields more accurate estimation of the components than alternatives.

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Hugo Richard, Pierre Ablin, Bertrand Thirion, Alexandre Gramfort, Aapo Hyvärinen. 2021-10-26. Shared Independent Component Analysis for Multi-Subject Neuroimaging. https://arxiv.org/abs/2110.13502

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