By using locally linear corrections, MNN can handle non-constant batch effects, here simulated as a small angle rotation of data on two-dimensional x-y coordinates. Each shown batch contains 400 cells (points). The reference batch is shown in red and the second (rotated) batch is shown in black for (a) raw (uncorrected) data and (b) data after MNN correction.

t-SNE plots of (a) the raw (uncorrected) simulated data, and the simulation data corrected by (b) our MNN approach, (c) limma and (d) ComBat. The filled circles and open triangles represent cells from the first and second batch respectively. The three different cell types are shown by different colours. While there is a split between cells of the same cell type in the uncorrected data, all batch correction methods remove the batch effect successfully for this simple example and yield clusters consistent with the original simulated cell types. The data were simulated to have identical cell type compositions (0.2/0.3/0.5) in both batches, with each batch containing 1000 cells.

t-SNE plots for (a) uncorrected data and data after correction by (b) our MNN approach, (c) limma and (d) ComBat. Cells are coloured according to their batch labels. (e) Histogram of the angle (f) between the first two SVD components of the reference data (SMART-seq2) and the correction vectors of the MARS-seq data calculated by MNN. Diffusion maps of the haematopoietic data after MNN correction, shown on the (f) first two diffusion components, (g) first and the third diffusion components, and (h) second and the third diffusion components.

t-SNE plots for (a) uncorrected data and data after correction by (b) MNN, (c) limma and (d) ComBat, coloured according to cell types. The same t -SNE plots are coloured according to batch for (e) uncorrected and batch-corrected data from (f) MNN, (g) limma and (h) ComBat. PCA plots for shared cell types (the SMART-seq2 batch with n=791 cells and the MARS-seq batch with n=2729 cells) between the two batches for (i) uncorrected data and batch-corrected data from (j) MNN, (k) limma and (l) ComBat.

t-SNE plots of (a) uncorrected data and data after correction by (b) MNN, (c) limma and (d) ComBat, coloured according to cell type labels. t-SNE plots were also generated for (e) uncorrected data and batch-corrected data from (f) MNN, (g) limma and (h) ComBat, coloured according to batch. PCA plots were also generated for (i) uncorrected and batch-corrected data from (j) MNN, (k) limma and (l) ComBat, coloured according to batch. Histograms of the angle between the batch effect vectors and the first two SVDs for the (m) reference (GSE85241) and the E-MTAB-5061 batch, (n) reference and the GSE86473 batch, and the (o) reference and the GSE81076 batch. (p) Silhouette coefficients according to cell type labels, with n=7096 (i.e. integrated number of cell from all four batches) observations for each boxplot. (q) Boxplots of the entropy of batch mixing on the first two PCs, with n=100 (i.e. number of bootstraps) observations for each boxplot. Boxes indicate median and first and third quartile, and whiskers extend to +/-1.5 times the interquartile ratio divided by the square root of the number of observations, and single points denote values outside this range.

t-SNE plots of (a) uncorrected data and data corrected by (b) our MNN approach, (c) limma and (d) ComBat, coloured according to cell type labels. t-SNE plots of (e) uncorrected data and batch-corrected data from (f) MNN, (g) limma and (h) ComBat, coloured according to batch. PCA plots of (i) uncorrected data and batch-corrected data from (j) MNN, (k) limma and (l) ComBat, coloured according to batch. Histogram of the angle between the batch effect vectors and the first two SVD components for the (m) reference (GSE85241) and the E-MTAB-5061 batch, (n) reference and the GSE86473 batch, and the (o) reference and the GSE81076 batch. (p) Silhouette coefficients according to cell type labels, with n=7096 (i.e. integrated number of cell from all four batches) observations for each boxplot. (q) Boxplots of the entropy of batch mixing on the first two PCs, with n=100 (i.e. number of bootstraps) observations for each boxplot. Boxes indicate median and first and third quartile, and whiskers extend to +/-1.5 times the interquartile ratio divided by the square root of the number of observations, and single points denote values outside this range.

t-SNE plots of pancreas data (GSE81076 with n=1007, GSE86473 with n= 2331, GSE85241 with n=1595 and E-MTAB-5061 with n=2163 cells) after batch correction with (a,c) MNN allowing for local batch vectors (default) or (b,d) MNN with a single global batch vector for all cells, coloured according to cell type labels (a,b) or batch (c,d). PCA plots of pancreas data after batch correction with (e) MNN allowing for local batch vectors (default) or (f) MNN with a single global batch vector for all cells, coloured according to batch. (g) Silhouette coefficients for clustering according to cell types after correction with two alternative settings of MNN, with n=7096 (i.e. integrated number of cell from all four batches) observations for each boxplot. The difference between the Silhouette coefficients is not significant (two-sided Welch's test p-value=0.97). (h) Entropy of batch mixing on the first two PCs for batch-corrected data with the two alternative settings of MNN, with n=100 (i.e. number of bootstraps) observations for each boxplot Allowing for local batch vectors has significantly (two-sided Welch's test p-value = 0.00001) larger entropy compared to the use of a global batch vector. Boxes indicate median and first and third quartile, and whiskers extend to +/-1.5 times the interquartile ratio divided by the square root of the number of observations, and single points denote values outside this range.

Supplementary Figures 1–7, Supplementary Notes 1–5 and Supplementary Table 1 (PDF 2875 kb)