@online{Fischer2301.13732,
TITLE = {Preserving Local Densities in Low-dimensional Embeddings},
AUTHOR = {Fischer, Jonas and Burkholz, Rebekka and Vreeken, Jilles},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2301.13732},
EPRINT = {2301.13732},
EPRINTTYPE = {arXiv},
YEAR = {2023},
MARGINALMARK = {$\bullet$},
ABSTRACT = {Low-dimensional embeddings and visualizations are an indispensable tool for<br>analysis of high-dimensional data. State-of-the-art methods, such as tSNE and<br>UMAP, excel in unveiling local structures hidden in high-dimensional data and<br>are therefore routinely applied in standard analysis pipelines in biology. We<br>show, however, that these methods fail to reconstruct local properties, such as<br>relative differences in densities (Fig. 1) and that apparent differences in<br>cluster size can arise from computational artifact caused by differing sample<br>sizes (Fig. 2). Providing a theoretical analysis of this issue, we then suggest<br>dtSNE, which approximately conserves local densities. In an extensive study on<br>synthetic benchmark and real world data comparing against five state-of-the-art<br>methods, we empirically show that dtSNE provides similar global reconstruction,<br>but yields much more accurate depictions of local distances and relative<br>densities.<br>},
}