Fig. 4

The diagram for integration of multimodal (triple) datasets by inClust+ (see details in Additional file 2). A The workflow. Training: ①Generation of the training dataset (Blue: gene expression from dataset 1; Green and red: protein abundance from dataset 1 and dataset 2; Purple: chromatin accessibility from dataset 2; Black: 0-value padding). ②Generation of the masked-input for the encoder in inClust+. ③Data encoding, covariates elimination and data integration. ④Reconstruction for data in all three modalities (Dark blue and yellow: reconstructed gene expression for dataset 1 and dataset 2; Light green and light red: reconstructed protein abundance for dataset 1 and dataset 2; Orange and Light purple: reconstructed chromatin accessibility for dataset 1 and dataset 2). ⑤Generation of the masked-output for loss calculation. ⑥Calculation of the loss for backpropagation. Data integration: after training, encoded low-dimensional representations are mixed together and clustered according to the cell types without the effect of covariate (batches and modalities). B–D Self-reconstruction. B In the first training phase, only gene expression data is effective for input (Blue long strip) and output (Dark blue 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 In the second and third training phases, only protein abundance data is effective for input (Green and red long strip) and output (Light green and light red long strip). Therefore, only the corresponding connections in the first layer (middle part) of the encoder and the last layer (middle part) of the decoder actually contribute to the training process. In short, inClust+ uses protein abundance data to reconstruct itself. D In the fourth training phase, only chromatin accessibility data is effective for input (Purple long strip) and output (Light purple long strip). Therefore, only the corresponding connections in the first layer (lower part) of the encoder and the last layer (lower part) of the decoder actually contribute to the training process. In short, inClust+ uses chromatin accessibility data to reconstruct itself. E, F alternative-reconstruction. E In the fifth training phase, only protein abundance data is effective for input (Green long strip) and gene expression data is effective for output (Dark blue long strip). Therefore, only the corresponding connections in the first layer (middle part) of the encoder and the last layer (upper part) of the decoder actually contribute to the training process. In short, inClust+ uses protein abundance data to reconstruct gene expression data. F In the sixth training phase, only protein abundance data is effective for input (Red long strip) and chromatin accessibility data is effective for output (Light purple long strip). Therefore, only the corresponding connections in the first layer (middle part) of the encoder and the last layer (lower part) of the decoder actually contribute to the training process. In short, inClust+ uses protein abundance data to reconstruct chromatin accessibility data