Parallel coordinates

Parallel coordinates is a common way of visualizing high-dimensional geometry and analyzing multivariate data.

To show a set of points in an n-dimensional space, a backdrop is drawn consisting of n parallel lines, typically vertical and equally spaced. A point in n-dimensional space is represented as a polyline with vertices on the parallel axes; the position of the vertex on the i-th axis corresponds to the i-th coordinate of the point.

History

Parallel coordinates were invented by Maurice d'Ocagne in 1885 .

The rotation of the axes is a translation in the parallel coordinates and if the lines intersected outside the parallel axes it can be translated between them by rotations. The simplest example of this is rotating the axis by 180 degrees. More details can be found at .

The necessity of scaling stems directly from the fact that the plot is based on interpolation (linear combination) of each consecutive variable.cite journal|author=R. Moustafa, E. Wegman|title=Multivariate continuousdata - Parallel Coordinates|journal= In: Unwin, A., Theus M., Hofmann, H.(Eds.), Graphics of Large Datasets: Visualizing a Million, Springer|pages= 143–156|year=2006] . Therefore, the variables must be in common scale, and there are many scaling methods to be considered as part of data perpetration process that can reveal more informative views.

Generalized Parallel Coordinates

The generalized parallel coordinate plot (GPCP) has been proposed by (Moustafa and Wegman 2002) cite journal|author=R. Moustafa, E. Wegman|title=One Some Generalizationto Parallel Coordinate Plot|journal=Seeing a million, A DataVisualization Workshop, Rain am Lech (nr.), Germany|year=2002] as a generalisation of parallel coordinates plots, based on parameter transformation. In this design, instead of plotting the raw data, it is transformed in some way first. If the interpolation function is piecewise lagrange, this cooresponds to the traditional PCP. If splines are used as the interpolation function, then the smooth parallel coordinate plot (SPCP) is achieved. In the smooth plot, every observation is mapped into a parametric line( or curve), which is smooth, continuous on the axes, and orthogonal to each parallel axis. cite journal|author=R. Moustafa, E. Wegman|title=Multivariate continuousdata - Parallel Coordinates|journal= In: Unwin, A., Theus M., Hofmann, H.(Eds.), Graphics of Large Datasets: Visualizing a Million, Springer|pages= 143–156|year=2006] .

This SPCP design gives a clear quantization level of each data attribute, that can best describe its distribution in complex situations, even with large data sets. Finally, if one uses the fourier interpolation of degree equals to the data dimensionality, then Andrews plot (Andrews 1972) is achieved. The GPCP design gives opportunities to researchers to explore alternative interpolation functions that best suited for particular application.

References

External links

* [http://www.futurepointsystems.com Future Point Systems] , creators of Starlight, a Visualization tool that includes a parallel coordinates display
* [http://www.math.tau.ac.il/~aiisreal Alfred Inselberg's Homepage] , with Visual Tutorial, History, Selected Publications and Applications
* [http://catt.okstate.edu/jones98/parallel.html A small, easy introduction] by Christopher V. Jones
* [http://www.agocg.ac.uk/reports/visual/casestud/brunsdon/abstract.htm An Investigation of Methods for Visualising Highly Multivariate Datasets] by C.Brunsdon, A.S.Fotheringham & M.E.Charlton, University of Newcastle, UK
* [http://www.ggobi.org/docs/parallel-coordinates// Parallel coordinates plot in GGobi]
* [http://www.amitgoel.com/pcoord/ Parallel Coordinates Visualization Applet]
* [http://www.dcs.napier.ac.uk/~marting/parCoord/GrahamKennedyParallelCurvesIV03.pdf Using Curves to Enhance Parallel Coordinate Visualisations] by Martin Graham & Jessie Kennedy, Napier University, Edinburgh, UK
* [http://www.galaxy.gmu.edu/stats/syllabi/inft979/GeneralizedParallelCoordinates.pdf On Some Generalization of Parallel Coordinate Plots] by Rida E. Moustafa and Edward J. Wegman (2002), George Mason University, Fairfax, VA
* [http://s92417348.onlinehome.us/software/dataloom/index.html Data Loom — a parallel coordinates visualisation tool for the Mac]
* [http://home.subnet.at/flo/mv/parvis/index.html parvis — a parallel coordinates tool] licensed under the GNU GPL - implemented in Java
* [http://www.wallinfire.net/picviz picviz — the graphviz of parallel coordinates] licensed under the GNU GPL v3 - implemented in C, with Python bindings used for the GUI.