# Imputation Methods for scRNA Sequencing Data
## 2 Imputation Methods
### Low-Ranked Matrix-Based Methods  
The method based on the low rank matrix identifies the potential spatial representation of the cell by capturing the linear relationship, and then reconstructs the expression matrix from the low rank that is no longer sparse. The availability links, programming language, whether a package is available, year of presentation, operative system, distribution compatibility and reference of the representative methods based on low-rank matrix see Table 3.  
Figure 6: The framework of SAVER method [26]. * 1. scRMD inputes the gene expression value by robust matrix decomposition (RMD). It reasonably decomposes the observed gene expression matrix into three contents: potential gene expression matrix, dropouts, and noise, and transforms the dropout value imputation problem into an optimization problem. The optimal gene expression value affected by dropout events is estimated by the alternating direction multiplier method, for more detail, please refer to Ref. [6]. We give a simple framework as shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Availability** & **Code** & **Pkg** & \begin{tabular}{c} **Operative System** \\ **and Distribution** \\ **Compatibility** \\ \end{tabular}  & **Year** & **Ref** \\ \hline CMF- & \begin{tabular}{c} [[http://bioconductor.org/packages/](http://bioconductor.org/packages/)]([http://bioconductor.org/packages/](http://bioconductor.org/packages/)) \\ release/bioc/html/SC3.html \\ (accessed on 1 October 2022) \\ \end{tabular}  & R & R & Linux, Mac and Windows & 2020 & [70] \\ deepMc & \begin{tabular}{c} [[https://github.com/henberg-lab/](https://github.com/henberg-lab/)]([https://github.com/henberg-lab/](https://github.com/henberg-lab/)) \\ scRNA.seq.course (accessed on 1 October 2022) \\ \end{tabular}  & TeX/Perl/Dockerfile/ \begin{tabular}{c} NULL \\ R/CSS/Python/Other \\ \end{tabular}  & Windows and Unix & 2018 & [71] \\ netNMF-sc & \begin{tabular}{c} [[https://github.com/raphael-group/](https://github.com/raphael-group/)]([https://github.com/raphael-group/](https://github.com/raphael-group/)) \\ netNMF-sc (accessed on \\ 1 October 2022) \\ \end{tabular}  & Jupyter & NULL & NA & 2020 & [75] \\ PBLR & \begin{tabular}{c} [[https://github.com/amsszlh/PBLR](https://github.com/amsszlh/PBLR)]([https://github.com/amsszlh/PBLR](https://github.com/amsszlh/PBLR)) \\ (accessed on 1 October 2022) \\ \end{tabular}  & MATLAB/R & NULL & NA & 2021 & [72] \\ Randomly & \ \begin{tabular}{c} randomly (accessed on \\ 1 October 2022) \\ \end{tabular}  & Jupyter & Python & NA & 2020 & [76] \\ WEDGE &
\begin{tabular}{c} (\  
2. McImpute models the gene expression matrix as a low-rank matrix, takes the pre-processed gene expression matrix as the input of the Nuclear-norm minimization algorithm, and recovers the gene expression value of the complete matrix by solving non-convex optimization problems. A remarkable feature of McImpute is that it does not assume that gene expression follows a certain distribution, for more detail, please refer to Ref. [3]. We give a simple framework as shown in Figure 8.
3. PBLR is a bounded low-rank method based on cell subsets, it not only considers the information of cell heterogeneity and gene expression, but also uses the change of gene expression to impute dropouts. The PBLR first extracts the data for the selected high-variable genes, and calculates the three affinity matrices based on the Pearson, Spearman, and Cosine metrics, respectively. PBLR then learns the consensus matrix by performing SymNMF (symmetric non-negative matrix factorization) on the three affinity matrices INMF (incomplete NMF) of the sub-matrix of the selected genes. PBLR further infers cell sub-populations by performing a hierarchical clustering of the consensus matrix. Finally, PBLR estimates the expression upper bound for the  
Figure 8: The framework of McImpute method [3]. Figure 7: The framework of scRMD method [6].