Jointly embedding multiple single-cell omics measurements

Abstract

Many single-cell sequencing technologies are now available, but it is still difficult to apply multiple sequencing technologies to the same single cell. In this paper, we propose an unsupervised manifold alignment algorithm, MMD-MA, for integrating multiple measurements carried out on disjoint aliquots of a given population of cells. Effectively, MMD-MA performs an in silico co-assay by embedding cells measured in different ways into a learned latent space. In the MMD-MA algorithm, single-cell data points from multiple domains are aligned by optimizing an objective function with three components: (1) a maximum mean discrepancy (MMD) term to encourage the differently measured points to have similar distributions in the latent space, (2) a distortion term to preserve the structure of the data between the input space and the latent space, and (3) a penalty term to avoid collapse to a trivial solution. Notably, MMD-MA does not require any correspondence information across data modalities, either between the cells or between the features. Furthermore, MMD-MA's weak distributional requirements for the domains to be aligned allow the algorithm to integrate heterogeneous types of single cell measures, such as gene expression, DNA accessibility, chromatin organization, methylation, and imaging data. We demonstrate the utility of MMD-MA in simulation experiments and using a real data set involving single-cell gene expression and methylation data.

Unsupervised Topological Alignment for Single-Cell Multi-Omics Integration

“…Manifold alignment is one of the foremost research fields of machine learning and data science [21,22,23,24,25,26,13,11]. In this study, we develop UnionCom, the unsupervised topological alignment method for single-cell multi-omics data integration.…”

“…Seurat v3 [5] 10.00 50.00 scAlign [7] 58.33 59.50 MMD-MA [11] 92 (see upper right panels of Fig. 2(a,b)) and well-matched branches (see lower right panels of Fig.…”

“…MAGAN [10] integrated single-cell multi-omics datasets by aligning the biological manifolds via a generative adversarial networks (GANs) approach. However, it lacked power in unsupervised task when the correspondence information among samples across datasets is unavailable [11]. Harmonic [12] aligned the diffusion geometries across datasets based on diffusion map method, but it required partial feature correspondence information.…”

“…Harmonic [12] aligned the diffusion geometries across datasets based on diffusion map method, but it required partial feature correspondence information. MMD-MA [11], an unsupervised manifold alignment algorithm for single-cell multi-omics datasets, embeds the latent biological low-dimensional structures in Reproducing Kernel Hilbert spaces (RKHSs), and found a shared common subspace of the RKHSs for manifold alignment by minimizing the maximum mean discrepancy (MMD) across modalities.…”

SCIM: Universal Single-Cell Matching with Unpaired Feature Sets

“…MATCHER (Welch et al, 2017) is based on a gaussian process latent variable model (GPLVM) (Lawrence, 2004) that can integrate technologies if their underlying latent structures can be represented in one dimension, applicable, for example, to model monotonic temporal processes. Other yet unpublished methods, such as MMD-MA (Liu et al, 2019) and UnionCom (Cao et al, 2020), rely on large kernel matrices which limit their scalability when using datasets of the sizes generally produced by molecular profiling.…”