Next, we repeated the procedure (PCA, mutual KNN, clustering) with modifications as follows. First, for computing the PCA transform, we limited the number of cells from the largest clusters to contribute max 20% of the total cells (to avoid skewing the PCA toward dominant cell types; note that we still kept all cells in the dataset, only masking those cells when computing the PCA transformation matrix). Second, we computed a balanced KNN as before but we assigned weights wi,j=1/kα, where k is the rank of j among the neighbors of i and a is a power that sets the scale of the weights. Large values of a will emphasize local neighborhoods, whereas smaller values will emphasize global structure, but in both cases, both local and global structures are accounted for. For practical purposes, we calculated the multiscale graph only up to k = 100 (beyond which the edge weights are vanishing), and we used a = 1. Using a fixed maximal k also ensured that the algorithm remained linear in the number of cells. We call this a multiscale KNN,
