块状缺失模式下的多源数据集成全局同步

中文摘要 AI 辅助

多源数据集成问题涉及来自不同来源、覆盖不同但可能重叠的实体集合的数据集，在基因组学、单细胞分析和医疗健康研究等许多现实领域中变得越来越重要。在这类问题中，人们通常首先学习每个来源内实体的低维表示，然后跨来源整合这些表示。由于不同来源的表示仅在某个变换下可识别，如何利用来源间的重叠实体来对齐这些表示成为一个关键挑战。现有方法以顺序或树状结构的方式对齐来源，因此对所选顺序敏感，并且仅利用了部分可用的重叠信息。受此局限性的启发，我们提出了全局同步多矩阵整合（GSMMI），该方法将对齐问题表述为全局同步问题，并利用所有两两重叠一次性联合对齐所有来源，从而充分利用跨来源的所有重叠信息。我们为GSMMI开发了一种高效的迭代算法，该算法快速且可扩展至这些应用中产生的大规模数据。我们从理论和实证两方面表明，GSMMI提高了对齐精度，即使在适度的重叠结构下也有明显改进。此外，我们将GSMMI开发为广泛适用于各种数据类型，涵盖对称半正定、对称不定以及非对称或矩形矩阵，甚至适用于来源仅在行或仅在列上重叠的设置，使其适用于多种应用场景。

英文摘要

Multi-source data integration problems over datasets from different sources covering different but possibly overlapping sets of entities have become increasingly important in many real-world areas, including genomics, single-cell analysis, and healthcare research. In such problems, one often first learns a low-dimensional representation of the entities within each source and then integrates these representations across sources. As the representations from different sources are only identifiable up to some transformation, how to align them across sources using the sources' overlapping entities becomes a key challenge. Existing methods align the sources in a sequential or tree-structured manner, and are therefore sensitive to the chosen order and exploit only part of the available overlapping information. Motivated by this limitation, we propose Global Synchronized Multiple Matrix Integration (GSMMI), which formulates this alignment problem as a global synchronization problem and jointly aligns all sources using all pairwise overlaps at once, thereby making full use of all overlapping information across the sources. We develop an efficient iterative algorithm for GSMMI that is fast and scalable to the large-scale data arising in these applications. We show both theoretically and empirically that GSMMI improves alignment accuracy, with clear improvements even under modest overlap structure. Moreover, we develop GSMMI to be broadly applicable across data types, covering symmetric positive semidefinite, symmetric indefinite, and asymmetric or rectangular matrices, and even settings where sources overlap only in their rows or only in their columns, making it suitable for a wide variety of application scenarios.

发表机构

• Stanford University（斯坦福大学）
• Johns Hopkins University（约翰斯·霍普金斯大学）

机构由 AI 辅助整理，请以论文原文为准。