基于伽玛-泊松分布和图正则化的单细胞非负矩阵分解算法

Single-cell Non-negative Matrix Factorization Algorithm Based on Gamma-Poisson Distribution and Graph Regularization

关键词:  单细胞RNA测序  降维  图正则化  伽玛-泊松分布  非负矩阵分解(NMF)

Key words:  scRNA-seq  dimensionality reduction  graph regularization  Gamma-Poisson distribution  Non-negative Matrix Factorization (NMF)

摘要:

单细胞RNA测序(Single-cell RNA sequencing,scRNA-seq)可以获取单细胞水平的基因表达谱。然而，目前许多基于非负矩阵分解(Non-negative Matrix Factorization,NMF)的降维算法在细胞类型识别中往往忽视了数据概率分布和细胞之间的拓扑关系，无法较好地兼顾数据的全局结构和局部结构。为了克服传统NMF降维算法在处理高维含噪稀疏数据时的不足，本文提出一种改进的单细胞非负矩阵分解算法GPNMF。GPNMF结合了伽玛-泊松(Gamma-Poisson)分布假设和图正则化技术，通过迭代更新因子分解矩阵以最小化重构误差，从而有效地保留数据的局部结构与全局结构。通过引入约束优化并稳定化模型，GPNMF在分解单细胞表达数据时能够提供更为稳健和可靠的结果。最后，利用真实scRNA-seq数据进行实验，验证了GPNMF的有效性，并展示了其在单细胞基因表达数据轨迹推断分析中的潜在应用。

Abstract:

Single-cell RNA sequencing (scRNA-seq) enables the acquisition of gene expression profiles at the single-cell level.However,many dimensionality reduction algorithms based on Non-negative Matrix Factorization (NMF) often overlook the probabilistic data distribution and topological relationships between cells,which result in a failure to adequately capture both the global and local structures of the data in cell type identification.To address the shortcomings of NMF methods in coping with sparsity,noise,and computational complexity in single-cell data,a Graph Regularized NMF (GPNMF) algorithm is proposed in this paper.The proposed method integrates the Gamma-Poisson distribution assumption with graph regularization.By iteratively updating the factorization matrices to minimize reconstruction errors,GPNMF effectively preserves both the local and global structures of the data.Through the introduction of constrained optimization and model stabilization,GPNMF yields more robust and reliable results in the decomposition of single-cell expression data.Finally,experiments conducted on real scRNA-seq datasets validate the effectiveness of GPNMF,demonstrating its potential applications in the trajectory inference analysis of single-cell gene expression data.