High-dimensional multimodal data arises in many scientific fields. The integration of multimodal data becomes challenging when there is no known correspondence between the samples and the features of different datasets. To tackle this challenge, we introduce AVIDA, a framework for simultaneously performing data alignment and dimension reduction. In the numerical experiments, Gromov-Wasserstein optimal transport and t-distributed stochastic neighbor embedding are used as the alignment and dimension reduction modules respectively. We show that AVIDA correctly aligns high-dimensional datasets without common features with four synthesized datasets and two real multimodal single-cell datasets. Compared to several existing methods, we demonstrate that AVIDA better preserves structures of individual datasets, especially distinct local structures in the joint low-dimensional visualization, while achieving comparable alignment performance. Such a property is important in multimodal single-cell data analysis as some biological processes are uniquely captured by one of the datasets. In general applications, other methods can be used for the alignment and dimension reduction modules.

翻译：高维多模态数据出现在许多科学领域中。当不同数据集的样本和特征之间没有已知对应关系时，多模态数据的集成变得具有挑战性。为应对这一挑战，我们提出AVIDA，这是一个同时进行数据对齐和降维的框架。在数值实验中，我们分别采用Gromov-Wasserstein最优传输和t分布随机近邻嵌入作为对齐和降维模块。我们证明，AVIDA能够正确对齐四个合成数据集和两个真实多模态单细胞数据集中缺乏共同特征的高维数据集。与现有几种方法相比，我们展示AVIDA在实现可比对齐性能的同时，更好地保留了单个数据集的结构，尤其是联合低维可视化中独特的局部结构。这一特性在多模态单细胞数据分析中尤为重要，因为某些生物过程仅由其中一个数据集唯一捕获。在一般应用中，其他方法也可用于对齐和降维模块。