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Pseudogrand tour

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The pseudogrand tour (PGT) is an approximate version of the grand tour (GT), and an example of the dynamic data visualization methods that assist in exploring hyperdimensional data through a continuous sequence of lower dimensional projections. The PGT adds the time dimensionality to the visualization process which in turn increases the human interaction with the data and reveals comprehensive views of the data. The PGT has some clear advantage suitable for the dynamic data visualization—such as the fast and easy computation, can be constructed using many orthogonal bases (interpolation functions), and the flexibility to visualize the projections as a sequence of scatterplot frames changing over time or a static profile plots of interpolated projections. This article focuses on the implementations of the PGT, the use of interpolation functions, the extensions to higher dimensions, and the scalability to large data points. WIREs Comp Stat 2010 2 711–718 DOI: 10.1002/wics.133

Figure 1.

The PGT for Wine data using Φλtλtλt − Ψλtλt + Ψλt, in (a), (b), (c), and (d), respectively. The classes are brushed with different colors and some projections reveal better separation of these classes, whereas some projections reveal outliers and so on. It is also possible to see some projections have higher variances and others have smaller ones.

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Figure 2.

The three‐dimensional PGT for Wine data using Φλtλtλt − Ψλtλt + Ψλt in (a), (b), (c), and (d), respectively. The classes are brushed with different colors and have some orthogonal spiral bands.

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Figure 3.

The PGT for Wine data at different angles (or time steps), t = −π/3,π/3. The class with green color distant itself form the other two classes in (a) and (c), whereas the class with orange color is distant from the other two in (b) and (d).

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Figure 4.

Imaging the PGT for Wine data using Φλtλtλt − Ψλtλt + Ψλt, in (a), (b), (c), and (d), respectively. Notice the homogenous color intensity on the y‐axes.

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Figure 5.

Discovering class properties and boundaries using enveloping method. We visualize \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\bar{Y}_t\pm c (var{Y}_t)=\bar{X}\Phi_t\pm c (\Phi_t^T\Sigma\Phi_t),$ \end{document} for each class for different value of c. As c decreases, the class separation increases, and for c = 0, we see class centroid's separations.

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Figure 6.

Detecting the hidden pattern in cluttered the PGT using QGPCP. The clutter effect on the PGT visualizing pollen data (data points in five dimensions) is shown in (a), whereas this effect is mitigated using QGPCP strategy in (b). We can clearly observe a fully saturated band of profiles in the plot, which is the hidden pattern in this data.

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