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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 will review some of these methods and discuss in detail the grand tour, which visualises high-dimensional distributions as animations of smoothly interpolated projections, allowing the viewer to extrapolate the shape of the parameter space in high dimensions. We can for example use the tour for the visualisation of multidimensional posterior distributions or to explore grouping in high dimension. I will then show how to use the idea of projection pursuit, i.e. searching the high-dimensional space for ’interesting’ low dimensional projections, to detect complex associations between multiple parameters. |
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