Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.8, pp. 330-331

Section Parallel-coordinates plots

C. J. Gilmore,a G. Barra and W. Donga*

aDepartment of Chemistry, University of Glasgow, University Avenue, Glasgow, G12 8QQ, UK
Correspondence e-mail: Parallel-coordinates plots

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A parallel-coordinates plot is a graphical data-analysis technique for plotting multivariate data. Usually orthogonal axes are used when doing this, but in parallel-coordinates plots orthogonality is abandoned and replaced with a set of N equidistant parallel axes, one for each variable and labelled X1, X2, X3,…, XN (Inselberg, 1985[link], 2009[link]; Wegman, 1990[link]). Each data point is plotted on each axis and the points are joined via a line connecting each data point. The data now become a set of lines. The lines are given the colours of the cluster to which they belong as defined by the current dendrogram. A parallel-coordinates display can be interpreted as a generalization of a two-dimensional scatterplot, and it allows the display of an arbitrary number of dimensions. The method can also be used to validate the clustering itself without using dendrograms. Using this technique it is possible to determine whether the clustering shown by the MMDS (or PCA) plot in three dimensions continues in higher dimensions.

Fig. 3.8.3[link] shows a typical example for a set of 80 organic samples partitioned into four clusters (Barr, Dong & Gilmore, 2009[link]). The plot shows that the clustering looks realistic when viewed in this way and that it is maintained when the data are examined in six dimensions.

[Figure 3.8.3]

Figure 3.8.3 | top | pdf |

Example of a parallel-coordinates plot in six dimensions, with axes labeled X1, X2, …, X6, for a set of 80 organic PXRD samples partitioned into four clusters. The plot shows that the clustering looks realistic and that it is maintained when the data are examined in six dimensions.


Barr, G., Dong, W. & Gilmore, C. J. (2009). PolySNAP3: a computer program for analysing and visualizing high-throughput data from diffraction and spectroscopic sources. J. Appl. Cryst. 42, 965–974.Google Scholar
Inselberg, A. (1985). The plane with parallel coordinates. Vis. Comput. 1, 69–91.Google Scholar
Inselberg, A. (2009). Parallel Coordinates. Visual multidimensional geometry and its applications. New York: Springer.Google Scholar
Wegman, E. J. (1990). Hyperdimensional data analysis using parallel coordinates. J. Am. Stat. Assoc. 85, 664–675.Google Scholar

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