A Multi-dimensional Joint ICA Model with Gaussian Copula

Abstract

Different imaging modalities can provide complementary information and fusing those can leverage their unique views into the brain. Independent component analysis (ICA) and its multimodal version, joint ICA (jICA), have been useful for brain imaging data mining. Conventionally, jICA assumes a common mixing matrix and independent latent joint components with independent and identical marginals. Thus, jICA maximizes a (melded) 1D distribution for each joint component, by either maximum likelihood or the infomax principle. In this study, we propose a joint ICA method that relaxes these assumptions by allowing samples from same voxels (in this case, fMRI and sMRI) to originate from a non-factorial bivariate distribution. We then maximize the likelihood of this joint 2D distribution. The full 2D bivariate distribution is defined by two marginal distributions linked with a copula. Several ICA-based studies on neuroimaging data have successfully modeled independent sources with a logistic distribution, providing robust and replicable results across modalities. This is because neuroimaging data often consists of rapid fluctuations around a baseline, resulting in super-Gaussian distributions. For consistency with prior literature, we choose the logistic distribution to model the marginals, combined with a Gaussian copula to model linkage via simple correlation. However, it should be noted that the proposed algorithm can easily adapt to different types of copulas and alternative marginal distributions. We demonstrated the performance of the proposed method on a simulated dataset and applied the proposed method to analyze structural and functional magnetic resonance imaging dataset from the Alzheimer’s disease neuroimaging initiative (ADNI) dataset.