An augmented GSNMF model for complete deconvolution of bulk RNA-seq data

Performing complete deconvolution analysis for bulk RNA-seq data to obtain both cell type specific gene expression profiles (GEP) and relative cell abundances is a challenging task. One of the fundamental models used, the nonnegative matrix factorization (NMF), is mathematically ill-posed. Although several of complete deconvolution methods have been developed and their estimates compared to ground truth for some datasets appear promising, a comprehensive understanding of how to circumvent the ill-posedness and improve solution accuracy is still lacking. In this paper, we first investigate the necessary requirements for a given dataset to satisfy the solvability conditions in NMF theory. Even with solvability conditions, the "unique" solutions of NMF are still subject to a rescaling matrix. Therefore, we provide estimates of the converged local minima and the possible rescaling matrix, based on informative initial conditions. Using these strategies, we develop a new pipeline of pseudo-bulk tissue data augmented, geometric structure guided NMF model (GSNMF+). In our approach, pseudo-bulk tissue data is generated, by statistical distribution simulated pseudo cellular compositions and single-cell RNAseq (scRNAseq) data, and then mixed with original dataset. The constituent matrices of the hybrid dataset then satisfy the weak solvability conditions of NMF. Furthermore, an estimated rescaling matrix is used to adjust minimizer of the NMF, which is expected to reduce mean square root errors of solutions. Our algorithms are tested on several realistic bulk-tissue dataset and have shown significant improvements in scenarios with singular cellular compositions.