Fig. 2

The diagram for integration of multiple monomodal (unpaired) data and subsequently gene imputation by inClust+ (see details in Additional file 2). A The workflow. Training: ①Generation of the training dataset. The data from scRNA-seq and MERFISH were aligned with common genes, and the missing scRNA-seq-specific genes in MERFISH data were filled with 0. ②Generation of the masked-input for the encoder in inClust+. ③Data encoding, covariates elimination and data integration. ④Reconstruction of expression profile for both common genes and scRNA-seq-specific genes. ⑤Generation of the masked-output for loss calculation. ⑥Calculation of the loss for backpropagation. Imputation: after training, the output of the decoder (step ④) would impute the missing scRNA-seq-specific genes in MERFISH data. B Training inClust+ with scRNA-seq data. In encoder, only the expression data of common genes are the effective inputs. So, in the first layer of the encoder, only the corresponding connections actually contribute to the encoding process. In decoder, both common genes and scRNA-seq-specific genes are reconstructed and pass through the mask. The loss between input and output with both the common and specific genes is calculated, and all connections in the last layer contribute to the loss. In short, inClust+ uses common genes to reconstruct common genes and scRNA-seq-specific genes. C Training inClust+ with MERFISH data. In encoder, only the expression data of common genes are the effective inputs. So, in the first layer of the encoder, only the corresponding connections actually contribute to the encoding process. In decoder, both common gene and scRNA-seq-specific gene are reconstructed, while the scRNA-seq-specific genes are filtered out by the output-mask. Loss is calculated according to the common genes, so only connections corresponding to common genes in the last layer of decoder contribute to the calculation of loss. In short, inClust+ uses common genes to reconstruct common genes. However, after training, inClust+ would output common genes and scRNA-seq-specific genes from the input of common genes