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. For this purpose, we propose contrastive independent component analysis (cICA). This generalizes independent component analysis to independent latent variables across a foreground and background. We propose a hierarchical tensor decomposition algorithm for cICA. We study the identifiability of cICA and demonstrate its performance visualizing data and finding patterns in data, using synthetic and real-world datasets, comparing the approach to existing contrastive methods.

翻译：在科学领域，数据可视化与数据模式发现是普遍存在的问题。越来越多的应用寻求在对比性场景中识别信号与结构：即相对于背景数据集的前景数据集。为此，我们提出了对比独立成分分析（cICA）。该方法将独立成分分析推广至前景与背景间独立的隐变量。我们提出了一种用于cICA的分层张量分解算法。我们研究了cICA的可识别性，并通过合成与真实数据集，将该方法与现有对比方法进行比较，展示了其在数据可视化和数据模式发现方面的性能。