Visualize your fitted non-linear dimension reduction model in the high-dimensional data space

Music City Center 

Non-linear dimension reduction (NLDR) techniques such as tSNE, UMAP provide a low-dimensional representation of high-dimensional data by applying non-linear transformation. The methods and parameter choices can create wildly different representations, so much so that it is difficult to decide which is best, or whether any or all are accurate or misleading. NLDR often exaggerates random patterns, sometimes due to the samples observed, but NLDR views have an important role in data analysis because, if done well, they provide a concise visual (and conceptual) summary of high dimensional distributions. To help evaluate the NLDR we have developed a way to take the fitted model, as represented by the positions of points in 2D, and turn it into a high-dimensional wireframe to overlay on the data, viewing it with a tour. Viewing a model in the data space is an ideal way to examine the fit. It is used here to help with the difficult decision on which 2D layout is the best representation of the high-dimensional distribution, or whether the 2D layout is displaying mostly random structure, and how different methods have same summary or particular quirks. Available in the R package `quollr`.

high-dimensional data vizualization

non-linear dimension reduction

tour 

Section on Statistical Graphics