  Single-cell RNA sequencing (scRNA-seq) is a relatively new technology that
has stimulated enormous interest in statistics, data science, and computational
biology due to the high dimensionality, complexity, and large scale associated
with scRNA-seq data. Nonnegative matrix factorization (NMF) offers a unique
approach due to its meta-gene interpretation of resulting low-dimensional
components. However, NMF approaches suffer from the lack of multiscale
analysis. This work introduces two persistent Laplacian regularized NMF
methods, namely, topological NMF (TNMF) and robust topological NMF (rTNMF). By
employing a total of 12 datasets, we demonstrate that the proposed TNMF and
rTNMF significantly outperform all other NMF-based methods. We have also
utilized TNMF and rTNMF for the visualization of popular Uniform Manifold
Approximation and Projection (UMAP) and t-distributed stochastic neighbor
embedding (t-SNE).
