Figure 1.

Illustration of the TransImpute (TransImp for short) computational framework

(A) TransImp is broadly a low-rank linear mapping, serving translation from scRNA-seq to ST data. The mapping matrix $\mathbf{W}$ (or its low-rank factorization $\mathbf{U}{\mathbf{V}}^T)$ will be achieved by using the overlapping genes between scRNA-seq and ST data. Once the mapping matrix is fitted, as denoted by $\hat{f}(·)$, it can be used to perform the inference of the unprobed genes in ST data.

(B) Quantification of the imputation uncertainty and how it can be predicted by a post hoc model. In the training stage, bootstrapping is performed by resampling SC cells locally within each cluster, creating multiple sampled references that are translated via fitted $\hat{f}(·)$ to ST data. Each ${\hat{\mathbf{Y}}}_S$ can be measured with a similarity score against the ground truth $\mathbf{Y}$, from which a “score variance” over bootstrapped samples can be computed for each gene in the training set. A linear-regression model is then fitted based on three independent variables to predict the variance. $X_{sparsity}$ is the proportion of zero count in scRNA-seq data for a gene, while ${\hat{Y}}_{mean}$ and ${\hat{Y}}_{var}$ are the mean and variance of the imputed ST gene expression from the non-bootstrapped original SC reference $\mathbf{X}$. At the inference stage, the linear model can predict the variance of imputed genes.