  Low-dimensional embeddings and visualizations are an indispensable tool for
analysis of high-dimensional data. State-of-the-art methods, such as tSNE and
UMAP, excel in unveiling local structures hidden in high-dimensional data and
are therefore routinely applied in standard analysis pipelines in biology. We
show, however, that these methods fail to reconstruct local properties, such as
relative differences in densities (Fig. 1) and that apparent differences in
cluster size can arise from computational artifact caused by differing sample
sizes (Fig. 2). Providing a theoretical analysis of this issue, we then suggest
dtSNE, which approximately conserves local densities. In an extensive study on
synthetic benchmark and real world data comparing against five state-of-the-art
methods, we empirically show that dtSNE provides similar global reconstruction,
but yields much more accurate depictions of local distances and relative
densities.
