  Muilti-modality data are ubiquitous in biology, especially that we have
entered the multi-omics era, when we can measure the same biological object
(cell) from different aspects (omics) to provide a more comprehensive insight
into the cellular system. When dealing with such multi-omics data, the first
step is to determine the correspondence among different modalities. In other
words, we should match data from different spaces corresponding to the same
object. This problem is particularly challenging in the single-cell multi-omics
scenario because such data are very sparse with extremely high dimensions.
Secondly, matched single-cell multi-omics data are rare and hard to collect.
Furthermore, due to the limitations of the experimental environment, the data
are usually highly noisy. To promote the single-cell multi-omics research, we
overcome the above challenges, proposing a novel framework to align and
integrate single-cell RNA-seq data and single-cell ATAC-seq data. Our approach
can efficiently map the above data with high sparsity and noise from different
spaces to a low-dimensional manifold in a unified space, making the downstream
alignment and integration straightforward. Compared with the other
state-of-the-art methods, our method performs better in both simulated and real
single-cell data. The proposed method is helpful for the single-cell
multi-omics research. The improvement for integration on the simulated data is
significant.
