Grand Tour (statistics)
The Grand Tour is a method for the exploratory analysis of high-dimensional multivariate data , which was first described by Daniel Asimov . It was then developed further by him and Andreas Buja .
In the Grand Tour, the data points are shown as a scatter diagram reduced to two or three dimensions and the display is rotated one after the other around one of the axes. After going through the three rotations, one of the dimensions that have not yet been investigated is added, but one that has already been considered is omitted and this is rotated around the axes and so on until all combinations of dimensions have been passed through at all viewing angles. In this way, the viewer can see the point cloud from every possible angle and from all sides.
The advantage of this method is that it is quickly possible to get an intuitive picture of the structure of the data and also to recognize non-linear relationships that would have been overlooked with classical, schematic multivariate methods such as analysis of variance or cluster analysis .
From a mathematical point of view, the data points are projected onto hyperplanes, each with two or three dimensions, and each possible such projection is run through one after the other. The Grand Tour is therefore related to the Projection Pursuit process . That it is sufficient to look at many low-dimensional projections of the data in order to understand the multivariate distribution is ensured by Cramér-Wold's theorem .
literature
- Dianne Cook, Andreas Buja, Javier Cabrera and Catherine Hurley: Grand Tour and Projection Pursuit . In: Journal of Computational and Graphical Statistics , IV, 3 (1995), pp. 155-172, JSTOR 1390844 .
- JD Salch, DW Scott: Data Exploration with the Density Grand Tour . In: Statistical Graphics and Computing Newsletter , ASA No. 8 (1997) pp. 7ff.
Web links
- GGobi: free software for statistical analysis (offers Grand Tour)