arXiv subjects

Michael Lydeamore

Publications and source records attributed to Michael Lydeamore.

3 recordsLinked to original sources

arXiv2025

quollr: An R Package for Visualizing 2-D Models from Nonlinear Dimension Reductions in High-Dimensional Space

Nonlinear dimension reduction methods provide a low-dimensional representation of high-dimensional data by applying a Nonlinear transformation. However, the complexity of the transformations and data structures can create wildly different representations depending on the method and hyper-parameter choices. It is difficult to determine whether any of these representations are accurate, which one is the best, or whether they have missed important structures. The R package quollr has been developed as a new visual tool to determine which method and which hyper-parameter choices provide the most accurate representation of high-dimensional data. The scurve data from the package is used to illustrate the algorithm. Single-cell RNA sequencing (scRNA-seq) data from mouse limb muscles are used to demonstrate the usability of the package.

stat.ME↗

arXiv2025

cardinalR: Generating Interesting High-Dimensional Data Structures

Simulated high-dimensional data is useful for testing, validating, and improving algorithms used in dimension reduction, supervised and unsupervised learning. High-dimensional data is characterized by multiple variables that are dependent or associated in some way, such as linear, nonlinear, clustering or anomalies. Here we provide new methods for generating a variety of high-dimensional structures using mathematical functions and statistical distributions organized into the R package cardinalR. Several example data sets are also provided. These will be useful for researchers to better understand how different analytical methods work and can be improved, with a special focus on nonlinear dimension reduction methods. This package enriches the existing toolset of benchmark datasets for evaluating algorithms.

stat.ME↗

arXiv2025

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

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.

stat.ME↗