Deep Nonnegative Matrix Factorization Using a Variational Autoencoder With Application to Single-Cell RNA Sequencing Data.

Single-cell RNA sequencing is used to analyze the gene expression data of individual cells, thereby adding to existing knowledge of biological phenomena. Accordingly, this technology is widely used in numerous biomedical studies. Recently, the variational autoencoder has emerged and has been adopted for the analysis of single-cell data owing to its high capacity to manage large-scale data. Many different variants of the variational autoencoder have been applied, and have yielded superior results. However, because it is nonlinear, the model does not provide parameters that can be used to explain the underlying biological patterns. In this paper, we propose an interpretable nonnegative matrix factorization method that decomposes parameters into those shared across cells and those that are cell-specific. Effective nonlinear dimension reduction was achieved via a variational autoencoder applied to the cell-specific parameters. In addition to achieving nonlinear dimension reduction, our model could estimate the cell-type-specific gene expression. To improve the estimation accuracy, we introduced log-regularization, which reflects the single-cell property. Overall, our approach displayed excellent performance in a simulation study and in real data analyses, while maintaining good biological interpretability.