The recent advent of high-throughput single-cell molecular profiling is revolutionizing biology and medicine by unveiling the diversity of cell types and states contributing to development and disease. The identification and characterization of cellular heterogeneity is typically achieved through unsupervised clustering, which crucially relies on a similarity metric. We here propose the use of Optimal Transport (OT) as a cell-cell similarity metric for single-cell omics data. OT defines distances to compare, in a geometrically faithful way, high-dimensional data represented as probability distributions. It is thus expected to better capture complex relationships between features and produce a performance improvement over state-of-the-art metrics. To speed up computations and cope with the high-dimensionality of single-cell data, we consider the entropic regularization of the classical OT distance. We then extensively benchmark OT against state-of-the-art metrics over thirteen independent datasets, including simulated, scRNA-seq, scATAC-seq and single-cell DNA methylation data. First, we test the ability of the metrics to detect the similarity between cells belonging to the same groups (e.g. cell types, cell lines of origin). Then, we apply unsupervised clustering and test the quality of the resulting clusters. In our in-depth evaluation, OT is found to improve cell-cell similarity inference and cell clustering in all simulated and real scRNA-seq data, while its performances are comparable with Pearson correlation in scATAC-seq and single-cell DNA methylation data. All our analyses are reproducible through the OT-scOmics Jupyter notebook available at https://github.com/ComputationalSystemsBiology/OT-scOmics.

https://www.biorxiv.org/content/biorxiv/early/2021/03/20/2021.03.19.436159.full.pdf

Optimal Transport improves cell-cell similarity inference in single-cell omics data

A formulation of the dataset integration problem describes the task of aligning two or more empirical distributions sampled from sources of the same kind, so that records of similar object end up close to one another. We propose a variant of the optimal transport (OT)- and Gromov-Wasserstein (GW)-based dataset integration algorithm introduced in SCOT [Demetci et al., 2020]. We formulate a constrained quadratic program to adjust sample weights before OT or GW so that weighted point density is close to be uniform over the point cloud, for a given kernel. We test this method with one synthetic and two real-life datasets from single-cell biology. Weights adjustment allows distributions with similar effective supports but different local densities to be reliably integrated, which is not always the case with the original method. This approach is entirely unsupervised, scales well to thousands of samples and does not depend on dimensionality of the ambient space, which makes it efficient for the analysis of single-cell datasets in biology. We provide an open-source implementation of this method in a Python package, woti.

https://biorxiv.org/content/10.1101/2021.05.12.443561v1.full.pdf

Unsupervised weights selection for optimal transport based dataset integration

Optimal Transport (OT) defines geometrically meaningful "Wasserstein" distances, used in machine learning applications to compare probability distributions. However, a key bottleneck is the design of a "ground" cost which should be adapted to the task under study. In most cases, supervised metric learning is not accessible, and one usually resorts to some ad-hoc approach. Unsupervised metric learning is thus a fundamental problem to enable data-driven applications of Optimal Transport. In this paper, we propose for the first time a canonical answer by computing the ground cost as a positive eigenvector of the function mapping a cost to the pairwise OT distances between the inputs. This map is homogeneous and monotone, thus framing unsupervised metric learning as a non-linear Perron-Frobenius problem. We provide criteria to ensure the existence and uniqueness of this eigenvector. In addition, we introduce a scalable computational method using entropic regularization, which - in the large regularization limit - operates a principal component analysis dimensionality reduction. We showcase this method on synthetic examples and datasets. Finally, we apply it in the context of biology to the analysis of a high-throughput single-cell RNA sequencing (scRNAseq) dataset, to improve cell clustering and infer the relationships between genes in an unsupervised way.

Geert-Jan Huizing

Papers

Unsupervised Ground Metric Learning using Wasserstein Eigenvectors.