To test the impact of sequencing depth and assay sensitivity on the performance of different scATAC-seq dimension reduction methods, we downsampled the total number of counts per cell from 100% (full dataset) down to 80%, 60%, 40% and 20% using the downsampleMatrix function from the DropletUtils R package67,68. For each downsampling, we re-ran each dimension reduction method (LSI (Signac), LSI (Cusanovich2018), LSI (log-TF), cisTopic (Warp-LDA), cisTopic (CGS), SnapATAC, SCALE), using default parameters for each method. For each downsampling, we estimated how well the data structure was preserved compared to the full dataset by computing the mean k-NN purity for each cell type in the dataset. This was defined as the fraction of k neighbors in the reduced-dimension space (LSI, cisTopic, SCALE or SnapATAC) for each cell i that belonged to the same annotated cell type as cell i, where cell types were predicted as described above using the gene expression assay. We computed nearest neighbors in each reduced-dimension space using the RANN R package (https://CRAN.R-project.org/package=RANN). For each dimension reduction method, we used the first 20 components removing any dimensions with
