Significance Visualizing data and finding patterns in data are ubiquitous problems in the sciences. Increasingly, applications seek signal and structure in a contrastive setting: a foreground dataset relative to a background dataset. The goal is to learn patterns and visualize the foreground after “subtracting off” the effect of the background. For this purpose, we propose contrastive independent component analysis (cICA). We investigate cICA theoretically and computationally. We find that, relative to other approaches, cICA is more expressive; that is, able to model a broader range of settings, while simultaneously being identifiable, able to recover patterns uniquely.