Multisource single‐cell data integration by MAW barycenter for Gaussian mixture models

One key challenge encountered in single‐cell data clustering is to combine clustering results of data sets acquired from multiple sources. We propose to represent the clustering result of each data set by a Gaussian mixture model (GMM) and produce an integrated result based on the notion of Wasserstein barycenter. However, the precise barycenter of GMMs, a distribution on the same sample space, is computationally infeasible to solve. Importantly, the barycenter of GMMs may not be a GMM containing a reasonable number of components. We thus propose to use the minimized aggregated Wasserstein (MAW) distance to approximate the Wasserstein metric and develop a new algorithm for computing the barycenter of GMMs under MAW. Recent theoretical advances further justify using the MAW distance as an approximation for the Wasserstein metric between GMMs. We also prove that the MAW barycenter of GMMs has the same expectation as the Wasserstein barycenter. Our proposed algorithm for clustering integration scales well with the data dimension and the number of mixture components, with complexity independent of data size. We demonstrate that the new method achieves better clustering results on several single‐cell RNA‐seq data sets than some other popular methods.