Year: 2025
Type: preprint
Abstract: Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR views have an important role in data analysis because, if done well, they provide a concise visual (and conceptual) summary of $p\text{-}D$ distributions. The NLDR methods and hyper-parameter choices can create wildly different representations, making it difficult to decide which is best, or whether any or all are accurate or misleading. To help assess the NLDR and decide on which, if any, is the most reasonable representation of the structure(s) present in the $p\text{-}D$ data, we have developed an algorithm to show the $2\text{-}D$ NLDR model in the $p\text{-}D$ space, viewed with a tour, a movie of linear projections. From this, one can see if the model fits everywhere, or better in some subspaces, or completely mismatches the data. Also, we can see how different methods may have similar summaries or quirks.
Source: arXiv (Cornell University)
Authors: Gamage, Jayani P., Cook, Dianne, Harrison, Paul, Lydeamore, Michael, Talagala, Thiyanga S.
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6929206200
Cites:
Cited by:
Related to: