Preserving local densities in low-dimensional embeddings
This addresses a critical issue for researchers in biology and data analysis who rely on embeddings for visualization, as it prevents misinterpretation of density artifacts, though it is an incremental improvement over existing methods.
The paper tackles the problem that popular low-dimensional embedding methods like tSNE and UMAP fail to preserve local density properties, showing that apparent cluster size differences can be computational artifacts. They propose dtSNE, which approximately conserves local densities, and demonstrate on synthetic and real-world data that it provides similar global reconstruction but much more accurate local distances and relative densities compared to five state-of-the-art methods.
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.