Contrastive independent component analysis for salient patterns and dimensionality reduction

In recent years, there has been growing interest in jointly analyzing a foreground dataset, representing an experimental group, and a background dataset, representing a control group. The goal of such contrastive investigations is to identify salient features in the experimental group relative to the control. Independent component analysis (ICA) is a powerful tool for learning independent patterns in a dataset. We generalize it to contrastive ICA (cICA). For this purpose, we devise a linear algebra-based tensor decomposition algorithm, which is more expressive but just as efficient and identifiable as other linear algebra-based algorithms. We establish the identifiability of cICA and demonstrate its performance in finding patterns and visualizing data, using synthetic, semisynthetic, and real-world datasets, comparing the approach to existing methods.