Unsupervised manifold alignment for single-cell multi-omics data

Integrating single-cell measurements that capture different properties of the genome is vital to extending our understanding of genome biology. This task is challenging due to the lack of a shared axis across datasets obtained from different types of single-cell experiments. For most such datasets, we lack corresponding information among the cells (samples) and the measurements (features). In this scenario, unsupervised algorithms that are capable of aligning single-cell experiments are critical to learning an in silico co-assay that can help draw correspondences among the cells. Maximum mean discrepancy-based manifold alignment (MMD-MA) is such an unsupervised algorithm. Without requiring correspondence information, it can align single-cell datasets from different modalities in a common shared latent space, showing promising results on simulations and a small-scale single-cell experiment with 61 cells. However, it is essential to explore the applicability of this method to larger single-cell experiments with thousands of cells so that it can be of practical interest to the community. In this paper, we apply MMD-MA to two recent datasets that measure transcriptome and chromatin accessibility in ~2000 single cells. To scale the runtime of MMD-MA to a more substantial number of cells, we extend the original implementation to run on GPUs. We also introduce a method to automatically select one of the user-defined parameters, thus reducing the hyperparameter search space. We demonstrate that the proposed extensions allow MMD-MA to accurately align state-of-the-art single-cell experiments.