How we see high-dimensions in statistics..

Increasing dimension adds an additional orthogonal axis.

If you want more high-dimensional shapes there is an R package, geozoo, which will generate cubes, spheres, simplices, mobius strips, torii, boy surface, enneper surface, dini surface, klein bottles, cones, various polytopes, ...

Philosophy

• It is common to show the data in the model space, for example, predicted vs observed plots for regression, linear discriminant plots, and principal components.
• By displaying the model in the high-d data space, rather than low-d summaries of the data produced by the model, we expect to better understand the fit.

Wickham et al (2015) Visualizing statistical models: Removing the blindfold, SAM

Hierarchical clustering

Dendrogram: data in the model space

Model in the data space

Summary

• The tourr package is available for you to look beyond 2D
• High-dimensional shapes, how they are defined, what they look like, how they differ is interesting
• Think about ways to look at the model in the data space

Multidimensional physics

You can read what we are doing with physics data here:

Dynamical projections for the visualization of PDFSense data

Dianne Cook, Ursula Laa, German Valencia

Further reading

• Buja et al (2004) Computational Methods for High-Dimensional Rotations in Data Visualization
• Cook, D., and Swayne, D. Interactive and Dynamic Graphics for Data Analysis with examples using R and GGobi
• Wickham et al (2011) tourr: An R Package for Exploring Multivariate Data with Projections
• Wickham et al (2015) Visualising Statistical Models: Removing the Blindfold (with Discussion), Statistical Analysis and Data Mining.
• Schloerke, et al (2016) Escape from Boxland