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We consider shared response modeling, a multi-view learning problem where onewants to identify common components from multiple datasets or views. Weintroduce Shared Independent Component Analysis (ShICA) that models each viewas a linear transform of shared independent components contaminated by additiveGaussian noise. We show that this model is identifiable if the components areeither non-Gaussian or have enough diversity in noise variances. We then showthat in some cases multi-set canonical correlation analysis can recover thecorrect unmixing matrices, but that even a small amount of sampling noise makesMultiset CCA fail. To solve this problem, we propose to use jointdiagonalization after Multiset CCA, leading to a new approach called ShICA-J.We show via simulations that ShICA-J leads to improved results while being veryfast to fit. While ShICA-J is based on second-order statistics, we furtherpropose to leverage non-Gaussianity of the components using amaximum-likelihood method, ShICA-ML, that is both more accurate and morecostly. Further, ShICA comes with a principled method for shared componentsestimation. Finally, we provide empirical evidence on fMRI and MEG datasetsthat ShICA yields more accurate estimation of the components than alternatives.

Shared Independent Component Analysis for Multi-Subject Neuroimaging