Unsupervised weights selection for optimal transport based dataset integration

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.