Unsupervised Topological Alignment for Single-Cell Multi-Omics Integration

Abstract

Single-cell multi-omics data provide a comprehensive molecular view of cells. However, single-cell multi-omics datasets consist of unpaired cells measured with distinct unmatched features across modalities, making data integration challenging. In this study, we present a novel algorithm, termed UnionCom, for the unsupervised topological alignment of single-cell multiomics integration. UnionCom does not require any correspondence information, either among cells or among features. It first embeds the intrinsic low-dimensional structure of each single-cell dataset into a distance matrix of cells within the same dataset and then aligns the cells across single-cell multi-omics datasets by matching the distance matrices via a matrix optimization method. Finally, it projects the distinct unmatched features across single-cell datasets into a common embedding space for feature comparability of the aligned cells. To match the complex nonlinear geometrical distorted low-dimensional structures across datasets, UnionCom proposes and adjusts a global scaling parameter on distance matrices for aligning similar topological structures. It does not require one-to-one correspondence among cells across datasets, and it can accommodate samples with dataset-specific cell types. UnionCom outperforms state-of-theart methods on both simulated and real single-cell multi-omics datasets. UnionCom is robust to parameter choices, as well as subsampling of features. UnionCom software is available at

Unsupervised manifold alignment for single-cell multi-omics data

“…Year Approach Problem Supervised JLMA [2] 2011 Eigenvalue decomposition on joint Laplacian Embedding No GUMA [4] 2014 Optimize geometry matching and feature matching Matching No MATCHER [5] 2015 Gaussian process to 1D trajectory Embedding No MAGAN [6] 2018 Generative adversarial network Matching Yes LIGER [7] 2019 Non-negative matrix factorization Embedding Yes Seurat v3 [8] 2019 Canonical correlation analysis Embedding Yes MMD-MA [9] 2019 Optimize maximum mean discrepancy Embedding No UnionCom [3] 2020 Optimize geometry matching and global scaling Embedding No Table 1: Algorithms for aligning multi-omic single-cell data.…”

“…Note that any embedding method can be adopted to also solve the matching task, simply by carrying out a matching procedure in the latent space. Conversely, it is possible to use a matching to induce an embedding [3].…”

“…The algorithm aims to learn two matchings: not just a oneto-one correspondence between cells but also a one-to-one correspondence between features in the two domains. UnionCom [3] finds a matching between data sets using just the first matching term from GUMA. The optimization is extended to better handle datasets of different sizes, and non-linearity is introduced by running the matching on geodesic distances on a k-NN graph within each data set.…”

“…• UnionCom [3] requires tuning of four hyperparameters and we specified the following search grid for them: the number k ∈ {5, 10, 25, ..., n} (with increments of 25 after k = 25) of neighbors in the graph, the dimensionality p ∈ {3, 5, 10} of the embedding space, the trade-off parameter β ∈ {0.001, 0.005, 0.01, 0.5, 0.1, 0.5, 1, 5, 10} for the embedding, and a regularization coefficient ρ ∈ {0.001, 0.005, 0.01, 0.5, 0.1, 0.5, 1, 5, 10}.…”

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.…”