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Grand Tour (data visualisation)
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<h2 id="technical-description">Technical description</h2> <p>Each "view" (i.e., frame) of the animation is an <a href="/facts/Orthogonal_projection/sElXGkxD">orthogonal projection</a> of the data set onto a 2-dimensional subspace (of the Euclidean space R<i>p</i> where the data resides). The subspaces are selected by taking small steps along a continuous curve, parametrized by time, in the space of all 2-dimensional subspaces of R<i>p</i> (known as the <a href="/facts/Grassmannian/QcmgLRq8">Grassmannian</a> G(2,<i>p</i>)). To display these views on a computer screen, it is necessary to pick one particular rotated position of each view (in the plane of the computer screen) for display. This causes the positions of the data points on the computer screen to appear to vary continuously. Asimov showed that these subspaces can be selected so as to make the set of them (up to time <i>t</i>) increasingly close to all points in G(2,<i>p</i>), so that if the grand tour movie were allowed to run indefinitely, the set of displayed subspaces would correspond to a <a href="/facts/Dense_set/nPT9Yxao">dense subset</a> of G(2,<i>p</i>).<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a><a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> </p> <h2 id="software">Software</h2> <ul><li>The <a href="https://cran.r-project.org/web/packages/tourr/index.html">tourr</a> <a href="/facts/R_(programming_language)/LSrkr8K8">R</a> package implements geodesic interpolation and basis generation functions that allow you to create new tour methods from R.</li> <li>The <a href="https://pypi.org/project/datatour/">datatour</a> <a href="/facts/Python_(programming_language)/YbuGqofa">Python</a> package allows you to see your data in its native dimension.</li> <li></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Asimov, Daniel. (1985). The grand tour: a tool for viewing multidimensional data. SIAM journal on scientific and statistical computing, 6(1), 128–143. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Huh, Moon Yul, and Kiyeol Kim. (2002) Visualization of multidimensional data using modifications of the Grand Tour. Journal of Applied Statistics 29.5: 721–728. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>