Unsupervised manifold alignment for single-cell multi-omics data

Abstract

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.

Single-cell landscape of nuclear configuration and gene expression during stem cell differentiation and X inactivation

“…Considering that both experimental approaches appear to recapitulate the developmental trajectory and maleto-female difference ( We successfully aligned cells based on non-allelic expression and chromatin accessibility patterns from F121 cells, as described in a separate publication (Singh et al 2020). Here, we investigated whether we could extend our alignments between sci-RNA-seq and sci-ATAC-seq data to allelic data, and also to sci-Hi-C data.…”

“…To align the F121 cells, which have sci-RNA, sci-ATAC and sci-Hi-C data at five time points, we employed the Maximum Mean Discrepancy Manifold Alignment (MMD-MA) algorithm (J. Liu et al 2019;Singh et al 2020).…”

“…Prior to alignment, each of the aforementioned count matrices were decomposed into topic-by-cell and feature-by-topic matrices using cisTopic (Bravo González-Blas et al 2019)). The topic-by-cell matrices served as input to the MMD-MA algorithm, as in (Singh et al 2020). A key assumption of MMD-MA is that the data is sampled from the same underlying distribution, so before applying MMD-MA to our sci-RNA-seq and sci-ATACseq measurements, we first subsampled the cells from the five time-points (d0, d3, d7, d11, NPCs) to ensure that the fraction of cells in each time-point was consistent across the two datasets (Supplementary Table 5).…”

“…To select hyperparameters, including the number of dimensions of the shared latent space, we optimized the segregation of cells by their respective time points. We optimized the MMD-MA algorithm for the range of hyperparameters used in (Singh et al 2020), including the size of the latent space in which the two datasets were aligned (Supplementary Table 5).…”

Manifold alignment for heterogeneous single-cell multi-omics data integration using Pamona

“…Recently, manifold alignment approaches, which aimed to align embedded low-dimensional manifolds, have been developed for holistic representation of the intrinsic cellular structures across cellular modalities, without requiring any correspondence information, either among cells or among features, e.g., MATCHER [6], MMD-MA [7,8], UnionCom [9], and SCOT [10]. These methods were derived under various advanced machine learning techniques, such as linear trajectory alignment using the latent Gaussian process, as in MATCHER [6]; kernel space matching based on maximum mean discrepancy, as in MMD-MA [7]; metric space matching based on the graphmatching/quadratic assignment formulation, as in UnionCom [9], or the optimal transport formulation, as in SCOT [10].…”