As advances in technology allow the acquisition of complementary information, it is increasingly common for scientific studies to collect multiple datasets. Large-scale neuroimaging studies often include multiple modalities (e.g., task functional MRI, resting-state fMRI, diffusion MRI, and/or structural MRI), with the aim to understand the relationships between datasets. In this study, we seek to understand whether regions of the brain activated in a working memory task relate to resting-state correlations. In neuroimaging, a popular approach uses principal component analysis for dimension reduction prior to canonical correlation analysis with joint independent component analysis, but this may discard biological features with low variance and/or spuriously associate structure unique to a dataset with joint structure. We introduce Simultaneous Non-Gaussian component analysis (SING) in which dimension reduction and feature extraction are achieved simultaneously, and shared information is captured via subject scores. We apply our method to a working memory task and resting-state correlations from the Human Connectome Project. We find joint structure as evident from joint scores whose loadings highlight resting-state correlations involving regions associated with working memory. Moreover, some of the subject scores are related to fluid intelligence.