Unsupervised latent variable models—blind source separation (BSS) especially—enjoy a strong reputation for their interpretability. But they seldom combine the rich diversity of information available in multiple datasets, even though multidatasets yield insightful joint solutions otherwise unavailable in isolation. We present a direct, principled approach to multidataset combination that takes advantage of multidimensional subspace structures. In turn, we extend BSS models to capture the underlying modes of shared and unique variability across and within datasets. Our approach leverages joint information from heterogeneous datasets in a flexible and synergistic fashion. We call this method multidataset independent subspace analysis (MISA). Methodological innovations exploiting the Kotz distribution for subspace modeling, in conjunction with a novel combinatorial optimization for evasion of local minima, enable MISA to produce a robust generalization of independent component analysis (ICA), independent vector analysis (IVA), and independent subspace analysis (ISA) in a single unified model. We highlight the utility of MISA for multimodal information fusion, including sample-poor regimes ( $N = 600$ ) and low signal-to-noise ratio, promoting novel applications in both unimodal and multimodal brain imaging data.

中文翻译：

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多数据集独立子空间分析在多模态融合中的应用

无监督的潜在变量模型——尤其是盲源分离 (BSS)——因其可解释性而享有盛誉。但它们很少结合多个数据集中可用的丰富信息，即使多数据集产生有洞察力的联合解决方案，否则单独无法获得。我们提出了一种利用多维子空间结构进行多数据集组合的直接、有原则的方法。反过来，我们扩展 BSS 模型以捕获数据集之间和数据集内共享和独特可变性的潜在模式。我们的方法以灵活和协同的方式利用来自异构数据集的联合信息。我们称这种方法为多数据集独立子空间分析（MISA）。利用 Kotz 分布进行子空间建模的方法创新，结合用于逃避局部最小值的新型组合优化，使 MISA 能够在单个统一模型中生成独立分量分析 (ICA)、独立向量分析 (IVA) 和独立子空间分析 (ISA) 的稳健泛化。我们强调了 MISA 在多模态信息融合中的效用，包括样本贫乏的制度（ $N = 600$ ) 和低信噪比，促进了单模态和多模态脑成像数据的新应用。