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 new 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, semi-synthetic, and real-world datasets, comparing the approach to existing methods.

翻译：近年来，联合分析代表实验组的前景数据集与代表对照组的背景数据集的研究日益受到关注。此类对比研究的目标是识别实验组相对于对照组的显著特征。独立成分分析（ICA）是学习数据集中独立模式的强大工具。我们将其推广为对比独立成分分析（cICA）。为此，我们设计了一种新的基于线性代数的张量分解算法，该算法更具表达力，但与其他基于线性代数的算法一样高效且可识别。我们建立了cICA的可识别性，并使用合成、半合成和真实世界数据集，通过将本方法与现有方法进行比较，展示了其在发现模式和可视化数据方面的性能。