Spectral clustering of single-cell multi-omics data on multilayer graphs

Motivation: Single-cell sequencing technologies that simultaneously generate multimodal cellular profiles present opportunities for improved understanding of cell heterogeneity in tissues. How the multimodal information can be integrated to obtain a common cell type identification, however, poses a computational challenge. Multilayer graphs provide a natural representation of multi-omic single-cell sequencing datasets, and finding cell clusters may be understood as a multilayer graph partition problem. Results: We introduce two spectral algorithms on multilayer graphs, spectral clustering on multilayer graphs and the weighted locally linear (WLL) method, to cluster cells in multi-omic single-cell sequencing datasets. We connect these algorithms through a unifying mathematical framework that represents each layer using a Hamiltonian operator and a mixture of its eigenstates to integrate the multiple graph layers, demonstrating in the process that the WLL method is a rigorous multilayer spectral graph theoretic reformulation of the popular Seurat weighted nearest neighbor (WNN) algorithm. Implementing our algorithms and applying them to a CITE-seq dataset of cord blood mononuclear cells yields results similar to the Seurat WNN analysis. Our work thus extends spectral methods to multimodal single-cell data analysis.