New Interactive Visual Tools and Statistical Methodology for Selecting and Evaluating Nonlinear Dimension Reduction Layouts of High-Dimensional Data

High-dimensional data, where each observation is described by many features, is common in fields such as bioinformatics, ecology, and forensic science. To visualise these data, researchers often reduce them to lower dimensions, typically to two, using linear and non-linear techniques. However, popular non-linear methods can sometimes distort or "hallucinate" patterns that do not actually exist. This research develops a new methodology to help users assess the reliability of these visualisations, and examines common mistakes people make when selecting a non-linear representation. The work is fully reproducible, with several software packages made available on the Comprehensive R Archive Network, and several web applications hosted at Monash.