  We propose a method called integrated diffusion for combining multimodal
datasets, or data gathered via several different measurements on the same
system, to create a joint data diffusion operator. As real world data suffers
from both local and global noise, we introduce mechanisms to optimally
calculate a diffusion operator that reflects the combined information from both
modalities. We show the utility of this joint operator in data denoising,
visualization and clustering, performing better than other methods to integrate
and analyze multimodal data. We apply our method to multi-omic data generated
from blood cells, measuring both gene expression and chromatin accessibility.
Our approach better visualizes the geometry of the joint data, captures known
cross-modality associations and identifies known cellular populations. More
generally, integrated diffusion is broadly applicable to multimodal datasets
generated in many medical and biological systems.
