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. 2023 Oct 24;24:244. doi: 10.1186/s13059-023-03073-x

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© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 5 — Evaluation of integration performance in the presence of batch effects. A Simulation details for the constructed data with technical batches and biological batches. B Performance of cell type annotation and runtime in the presence of technical and biological batches shown in A. ARI and NMI measure agreement between predicted cell type and ground-truth labels. Runtime is measured in seconds, for each method, in log2 scale. Error bar is mean ± standard deviation. C Simulation details for two datasets with more complex batch structures. D Performance of cell type annotation and runtime in the presence of technical and biological batches shown in C. ARI and NMI measure agreement between predicted cell type and ground-truth labels. Runtime is measured in seconds, for each method, in log2 scale. Whisker is 1.5 times the inter-quartile range