LONMF: a non-negative matrix factorization model based on graph Laplacian and optimal transmission for paired single-cell multi-omics data integration.

The rapid development of single-cell sequencing technologies has provided a robust technical support for the efficient resolution of multiple levels of molecular information from a single-cell population. However, the data produced by these technologies often contain a lot of noise and differences in characteristics that make it difficult to integrate and analyze single-cell multi-omics data. In this study, there is a growing demand for methods to integrate single-cell multi-omics data, which is expected to enhance the ability to reveal cellular heterogeneity and provide new biological perspectives for a deeper understanding of cellular phenotypes by jointly analyzing multi-omics data. We propose LONMF, a non-negative matrix factorization algorithm combining graph Laplacian and optimal transmission to enhance clustering performance and interpretability. We apply LONMF to visualize and cluster multi-pair single-cell multi-omics data, including 10X-multi-group, CITE-seq, and TEA-multi-group seq, to facilitate marker characterization and gene ontology enrichment analysis and to provide rich biological insights for downstream analyses. Our comprehensive benchmarking demonstrates that LONMF exhibits comparable performance compared with the current state-of-the-art in cell clustering and outperforms other methods in terms of biological interpretability.