Preserving local densities in low-dimensional embeddings

Abstract

Low-dimensional embeddings and visualizations are an indispensable tool for analysis of high-dimensional data. State-of-the-art methods, such as T SNE 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 DT SNE, 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 DT - SNE provides similar global reconstruction, but yields much more accurate depictions of local distances and relative densities.