Data integration of single-cell measurements is critical for our understanding of cell development and disease, but the lack of correspondence between different types of single-cell measurements makes such efforts challenging. Several unsupervised algorithms are capable of aligning heterogeneous types of single-cell measurements in a shared space, enabling the creation of mappings between single cells in different data modalities. We present Single-Cell alignment using Optimal Transport (SCOT), an unsupervised learning algorithm that uses Gromov Wasserstein-based optimal transport to align single-cell multi-omics datasets. SCOT calculates a probabilistic coupling matrix that matches cells across two datasets. The optimization uses k-nearest neighbor graphs, thus preserving the local geometry of the data. We use the resulting coupling matrix to project one singlecell dataset onto another via a barycentric projection. We compare the alignment performance of SCOT with state-of-the-art algorithms on three simulated and two real datasets. Our results demonstrate that SCOT yields results that are comparable in quality to those of competing methods, but SCOT is significantly faster and requires tuning fewer hyperparameters. The code is available at https://github.com/rsinghlab/SCOT

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.

Data integration of single-cell measurements is critical for understanding cell development and disease, but the lack of correspondence between different types of measurements makes such efforts challenging. Several unsupervised algorithms can align heterogeneous single-cell measurements in a shared space, enabling the creation of mappings between single cells in different data domains. However, these algorithms require hyperparameter tuning for high-quality alignments, which is difficult in an unsupervised setting without correspondence information for validation. We present Single-Cell alignment using Optimal Transport (SCOT), an unsupervised learning algorithm that uses Gromov Wasserstein-based optimal transport to align single-cell multi-omics datasets. We compare the alignment performance of SCOT with state-of-the-art algorithms on four simulated and two real-world datasets. SCOT performs on par with state-of-the-art methods but is faster and requires tuning fewer hyperparameters. Furthermore, we provide an algorithm for SCOT to use Gromov Wasserstein distance to guide the parameter selection. Thus, unlike previous methods, SCOT aligns well without using any orthogonal correspondence information to pick the hyperparameters. Our source code and scripts for replicating the results are available at https://github.com/rsinghlab/SCOT.