We compared our method with nine leading scRNA-seq batch effect removal methods: ComBat, scVI, LIGER, fastMNN, BBKNN, Harmony, Scanorama, Seurat v3, and DESC. See Additional file 1: Table S2 for detailed version information. Combat and BBKNN correction were performed using the scanpy API “scanpy.pp.combat” and “scnpy.external.pp.bbknn.” scVI was run using the default parameters and obtained latent representations were used for further analysis. The “optimizeALS” parameter of LIGER was set to “k = 20.” We used the “SeuratWarpper” versions of fastMNN (“RunFastMNN”) and Harmony (“RunHarmony”). Scanorama was run using the default parameter of “scanorama.correct.” The dimensions parameters of Seurat v3 were all set to “dim = 1:30.” DESC was run with the default parameters, and especially the “louvain_resolution” was set as 1.0. Because some methods cannot give the corrected expression values, we compared them by using the UMAP embeddings. All embeddings were run by using the same parameters of the Python package “umap-learn.”

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