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# Grand tour and the Andrews plot

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The relationship between Andrews plot and Grand Tour (GT) stems from the fact that both view multiprojections of hyperdimensional data. The difference, however, is that GT views all possible projections of the data, while Andrews plot views only sets of projections. In this paper, we give a quick introduction to GT and Andrews plot and some visualization examples. Copyright © 2009 John Wiley & Sons, Inc.

Figure 1.

Andrews plot of Iris data using different normal vectors Φλt: (a) with λ = 1,2, and (b) with \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\lambda = 1, \sqrt{2}$\end{document}. Clearly, there is one highly separated class in this data (with red color) and two highly overlapped ones.

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Figure 2.

The 3D Andrews plot, \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$(y_{it} = \bf{x}_{i}^{T}\Phi_{\lambda t}, z_{it} = \bf{x}_{i}^{T}\Psi_{\lambda t}),$\end{document} with λi = i (a), and \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\lambda =(1, \sqrt{2})$\end{document} (b).

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Figure 3.

The 3D Andrews plot with \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$y_{it} = \bf{x}_{i}^{T}\Phi_{\lambda t}$\end{document} and \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$z_{it} = \bf{x}_{i}^{T} \Psi_{\lambda t}$\end{document}, where we use λi = i, in (a) and \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\lambda = (1, \sqrt{2}),$\end{document} in (b).

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Figure 4.

Andrews plot in 2D for the remote‐sensing data. The plot is severely cluttered and no information can be gained regarding any structure that might be in this data.

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