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 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 lacking. In this paper, we first investigated 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 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 developed a new pipeline of pseudo-bulk tissue data augmented, geometric structure guided NMF model (GSNMF$ + $). In our approach, pseudo-bulk tissue data was generated, by statistical distribution simulated pseudo cellular compositions and single-cell RNA-seq (scRNA-seq) data, and then mixed with the original dataset. The constituent matrices of the hybrid dataset then satisfy the weak solvability conditions of NMF. Furthermore, an estimated rescaling matrix was used to adjust the minimizer of the NMF, which was expected to reduce mean square root errors of solutions. Our algorithms are tested on several realistic bulk-tissue datasets and showed significant improvements in scenarios with singular cellular compositions.
Citation: Shaoyu Li, Su Xu, Xue Wang, Nilüfer Ertekin-Taner, Duan Chen. An augmented GSNMF model for complete deconvolution of bulk RNA-seq data[J]. Mathematical Biosciences and Engineering, 2025, 22(4): 988-1018. doi: 10.3934/mbe.2025036
Performing complete deconvolution analysis for bulk RNA-seq data to obtain both cell type specific gene expression profiles (GEP) and relative cell abundances is a challenging task. One of the fundamental models used, the nonnegative matrix factorization (NMF), is mathematically ill-posed. Although several complete deconvolution methods have been developed, and their estimates compared to ground truth for some datasets appear promising, a comprehensive understanding of how to circumvent the ill-posedness and improve solution accuracy is lacking. In this paper, we first investigated the necessary requirements for a given dataset to satisfy the solvability conditions in NMF theory. Even with solvability conditions, the "unique" solutions of NMF are subject to a rescaling matrix. Therefore, we provide estimates of the converged local minima and the possible rescaling matrix, based on informative initial conditions. Using these strategies, we developed a new pipeline of pseudo-bulk tissue data augmented, geometric structure guided NMF model (GSNMF$ + $). In our approach, pseudo-bulk tissue data was generated, by statistical distribution simulated pseudo cellular compositions and single-cell RNA-seq (scRNA-seq) data, and then mixed with the original dataset. The constituent matrices of the hybrid dataset then satisfy the weak solvability conditions of NMF. Furthermore, an estimated rescaling matrix was used to adjust the minimizer of the NMF, which was expected to reduce mean square root errors of solutions. Our algorithms are tested on several realistic bulk-tissue datasets and showed significant improvements in scenarios with singular cellular compositions.
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Shaoyu Li, Su Xu, Xue Wang, Nilüfer Ertekin-Taner, Duan Chen. An augmented GSNMF model for complete deconvolution of bulk RNA-seq data[J]. Mathematical Biosciences and Engineering, 2025, 22(4): 988-1018. doi: 10.3934/mbe.2025036
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