Choosing Better NLDR Layouts by Evaluating the Model in the High-dimensional Data Space

TL;DR

This paper introduces an algorithm that visualizes low-dimensional NLDR models within the original high-dimensional space using a tour, aiding in evaluating the quality and appropriateness of NLDR representations.

Contribution

It presents a novel method to assess NLDR layouts by visualizing the model in the high-dimensional space, helping identify fit quality and method differences.

Findings

Enables visualization of NLDR models in high-dimensional space

Assists in evaluating the accuracy of NLDR representations

Reveals similarities and quirks among different NLDR methods

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.