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.

翻译：低维嵌入与可视化是高维数据分析不可或缺的工具。诸如 tSNE 和 UMAP 等尖端方法擅长揭示高维数据中隐藏的局部结构，因此在生物学标准分析流程中常被采用。然而，我们表明这些方法无法重建局部性质，例如密度的相对差异（图1），并且聚类大小的表观差异可能源于不同样本量导致的计算伪像（图2）。针对这一问题，我们提出理论分析，并进而推荐 dtSNE，它近似保持局部密度。通过在合成基准数据与真实世界数据上与五种前沿方法进行广泛对比研究，我们凭经验证明，dtSNE 在提供类似的全局重构效果的同时，能更准确地描绘局部距离与相对密度。