  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.
