Fast and interpretable non-negative matrix factorization for atlas-scale single cell data

Abstract

Non-negative matrix factorization (NMF) is an intuitively appealing method to extract additive combinations of measurements from noisy or complex data. NMF is applied broadly to text and image processing, time-series analysis, and genomics, where recent technological advances permit sequencing experiments to measure the representation of tens of thousands of features in millions of single cells. In these experiments, a count of zero for a given feature in a given cell may indicate either the absence of that feature or an insufficient read coverage to detect that feature ("dropout"). Unlike spectral decompositions such as Singular Value Decomposition (SVD) or Principal Component Analysis (PCA), NMF is an ideal method for handling single-cell data with ambiguous zeros due to its strictly positive imputation of signal. While single-cell datasets contain many ambiguous zero counts, most analysis pipelines apply SVD or PCA on transformed counts because these implementations are fast and current NMF implementations are slow. We present an accessible NMF implementation that is much faster than PCA and rivals the runtimes of state-of-the-art SVD. NMF models learned with our implementation from raw count matrices yield intuitive summaries of complex biological processes, capturing coordinated gene activity and enrichment of sample metadata. Our NMF implementation, available in the RcppML (Rcpp Machine Learning library) R package, improves upon current NMF implementations by introducing a scaling diagonal to enable convex L1 regularization for feature engineering, reproducible factor scalings, and symmetric factorizations. RcppML NMF easily handles sparse datasets with millions of samples, making NMF an attractive replacement for PCA in the analysis of single-cell experiments.

Single cell RNA-seq by mostly-natural sequencing by synthesis

“…We calculated all NMF models with RcppML v0.3.7 46 using 15 factors and with the log TPM matrix as input including genes expressed in more than 1% of cells. NMF returns a cell loading matrix, with one row per cell and one column per factor, and a gene loading matrix, with one row per gene and one column per factor.…”

Deciphering Hematopoiesis at single cell level through the lens of reduced dimensions

“…PCA and ICA were performed using RunPCA and RunICA functions of Seurat, which uses IRLBA 35 and fastICA 36 for performing PCA and ICA, respectively. NMF was performed on a log-normalized count matrix using nmf function of an R package RcppML 37 . To correct the donor-specific batch effects, an R package harmony 38 was used in each case (i.e-PCA, ICA, and NMF).…”

Scalable and model-free detection of spatial patterns and colocalization

“…Non-negative matrix factorization is applied on spatially variable genes detected by SpaGene to identify distinct spatial patterns. NMF is implemented by the RcppML R package (DeBruine et al 2021). It is challenging to choose the optimal number of NMF factors.…”