Dimensionality reduction for single cell RNA sequencing data using constrained robust non-negative matrix factorization

Single cell RNA-sequencing (scRNA-seq) technology, a powerful tool for analyzing the entire transcriptome at single cell level, is receiving increasing research attention. The presence of dropouts is an important characteristic of scRNA-seq data that may affect the performance of downstream analyses, such as dimensionality reduction and clustering. Cells sequenced to lower depths tend to have more dropouts than those sequenced to greater depths. In this study, we aimed to develop a dimensionality reduction method to address both dropouts and the non-negativity constraints in scRNA-seq data. The developed method simultaneously performs dimensionality reduction and dropout imputation under the non-negative matrix factorization (NMF) framework. The dropouts were modeled as a non-negative sparse matrix. Summation of the observed data matrix and dropout matrix was approximated by NMF. To ensure the sparsity pattern was maintained, a weighted ℓ₁ penalty that took into account the dependency of dropouts on the sequencing depth in each cell was imposed. An efficient algorithm was developed to solve the proposed optimization problem. Experiments using both synthetic data and real data showed that dimensionality reduction via the proposed method afforded more robust clustering results compared with those obtained from the existing methods, and that dropout imputation improved the differential expression analysis.