Fig. 1

IDER metric accurately measures the biological similarity between cell groups. A Schematic diagram shows how the IDER metric measures the inter-group similarity. B The diagram shows the theoretical justification for CIDER. E_ijk denotes the expression level of gene j in cell i of batch k, z_ik cell assignment of cells of cell i, C cluster effect, B batch effect, and P patient effect or other biases. In the lower panel, z_ik is set to 1. C Schematic diagram of asCIDER and dnCIDER. d t-SNE plots show the cells from three batches of Dataset 1. Each subpanel represents a batch. Cells are colored by the population. Each batch-specific cluster is denoted by a label. E The IDER metric generated higher similarity between group pairs, (g₁, g₁’) and (g₂, g₂’), from identical cell types and lower similarity between group pairs from different cell types