Why should you not judge how similar two clusters are from their distance on a UMAP plot?

Why

Each cell is described by thousands of genes, or by 10 to 50 principal components after reduction. A two-dimensional picture cannot keep all those distances. The Bioconductor book explains that t-SNE and UMAP work hard to keep each cell's nearest neighbors together, so cells in one unbroken island were probably close in the full data.

It warns that nothing guarantees large distances are preserved, and that measuring gaps between islands to compare cell types would be courageous. Its advice is to cluster on the principal components and use the embedding only to display the result. Chari and Pachter went further in The specious art of single-cell genomics.

They found that even the neighbor sets in 2D embeddings differed strongly from those in the original space, with Jaccard distances above 0.8 on average, and argued that such plots are poor tools for quantitative conclusions. Settings matter too. Perplexity in t-SNE and the random seed change the picture, so the book suggests trying several values.

Use distances in PCA space, or marker genes, to compare clusters. Use the plot to see the overall layout and to color cells by a gene or a sample.