Abstract
In physics we often encounter high-dimensional data, in the form of multivariate measurements or of models with multiple free parameters. The information encoded is increasingly explored using machine learning, but is not typically explored visually. The barrier tends to be visualising beyond 3D, but systematic approaches for this exist in the statistics literature. I use examples from particle and astrophysics to show how we can use the “grand tour” for such multidimensional visualisations, for example to explore grouping in high dimension and for visual identification of multivariate outliers. I then discuss the idea of projection pursuit, i.e. searching the high-dimensional space for “interesting” low dimensional projections, and illustrate how we can detect complex associations between multiple parameters.
Highlights
Data visualisation is an important part of the statistical analysis of data, and can often provide insights beyond what is found with standard summary statistics
Visualisation is important in physics, where it is used to guide our intuition on phenomena beyond direct experience
To study this data we first group the experimental observations according to the type of measurement into: deep-inelastic scattering (DIS), vector boson production (VBP) and jet production measurements
Summary
Data visualisation is an important part of the statistical analysis of data, and can often provide insights beyond what is found with standard summary statistics. This is illustrated by Anscombe’s quartet [1], four datasets with the same statistical properties, including the mean and variance along each variable, as well as the correlation and regression line. We use visualisation for the analysis of our results, in order to understand and interpret them. It is a powerful method for diagnosing problems, and often preferred for communicating results. We show how the grand tour can be used to look at the data in more than three dimensions instead
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