Fig. 6

The diagram for cross-modal generation of inClust+ (see details in Additional file 2). A The workflow. Training: ①Generation of the training dataset (Blue, red and purple: gene expression from dataset 1, dataset 2 and dataset 3; Green and orange: protein abundance from dataset 1 and dataset 2; Black: 0-value padding).. ②Generation of the masked-input for the encoder in inClust+. ③Data encoding, covariates elimination and data integration. ④The decoder simultaneously outputs the reconstructed gene expression data and the reconstructed protein abundance data (Light blue, light red and light purple: reconstructed gene expression for dataset 1, dataset 2 and dataset 3; Light green, faint yellow and brown: reconstructed protein abundance for dataset 1, dataset 2 and dataset 3). ⑤Generation of the masked-output for loss calculation. ⑥Calculation of the loss for backpropagation. Label transfer and cross-modal generation: after training, the labels are transferred from cells of multimodal data to the cells of monomodal data in the same clusters. The output of the decoder (step ④) would generate the missing modality in monomodal data. B Training inClust+ with gene expression data. In these stages, only gene expression data is effective for input (Blue, red and purple long strip) and output (Light blue, light red and light purple long strip). Therefore, only the corresponding connections in the first layer (upper part) of the encoder and the last layer (upper part) of the decoder actually contribute to the training process. In short, inClust+ uses gene expression data to reconstruct itself. C Training inClust+ with gene expression data and translating them into protein abundance data. In these stages, only gene expression data is effective for input (Blue and red long strip) and protein abundance data is effective for output (Light green and faint yellow long strip). Therefore, only the corresponding connections in the first layer (upper part) of the encoder and the last layer (lower part) of the decoder actually contribute to the training process. In short, inClust+ uses gene expression data to reconstruct protein abundance data