Parallel coordinates

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Parallel coordinates is a common technique for representing high-dimensional data.

To show a set of points in an n-dimensional space, a backdrop is drawn consisting of n parallel line segments, typically vertical and with equal spacing between them. Then a given point in n-dimensional space is represented as a polyline with vertices on the parallel line segments; the position of the vertex on the i-th segment corresponds to the i-th coordinate of the point.

Adding more dimensions to the parallel coordinate plot simply involves adding more axes to the right of the plot and extending the line to join up with the new points forming a polygonal line from the first to the last parallel co-ordinate axis.

Part of the value of parallel coordinates is that certain geometrical properties in high dimensions translate into easily seen 2D properties. For example, a set of points that lie on a line in n-space will translate to a set of polylines in parallel coordinates that all intersect at a common point.

In 1990, the parallel coordinate plot (PCP) is introduced as a method for visualizing multivaraite data. Since that time, the technique became an important tool for those who attempt exploratory data analysis and visual data mining. It is worthnoting that, the PCP is developed based on the projective geometry view point.

Generalized Parallel Coordinate Plot (GPCP) (2001) is a relatively new design that is based on parameter transformation processes. In this design, data is transformed into the parameter space through interpolation functions (basis). If the interpolation function set to be the Piecewise Lagrange of degree one, then the traditional parallel coordinate plot (TPCP)is achieved, i.e. every data record is mapped into a broken line crosses the parallel axes in the parameter space. If the interpolation function set to be the Splines, then the smooth parallel coordinate plot is achieved. In the smooth plot, every observation is mapped into a parametric line/curve, which is a smooth, continuous on the axes, and orthogonal to each parallel axes. This unprecedent design gives a clear quantization level of each data attribute, that can best describe its distribution in complex situations, even with large data sets. The GPCP design gives opportunities to researchers to explore alternative interpolation functions and quick interpretation to such outcome.

External links

Visual Tutorial, History, Selected Publications, Applications :

http://www.math.tau.ac.il/~aiisreal

An Investigation of Methods for Visualising Highly Multivariate Datasets:

http://www.agocg.ac.uk/reports/visual/casestud/brunsdon/abstract.htm

Parallel Coordinates Visualization Applet: http://www.amitgoel.com/pcoord/
Using Curves to Enhance Parallel Coordinate Visualisations: http://www.dcs.napier.ac.uk/~marting/parCoord/GrahamKennedyParallelCurvesIV03.pdf
Visualizing hyperdimensional data using parallel coordinate plot, JASA, 85, 664--675, 1990.

On Some Generalization of Parallel Coordinate Plot: www.galaxy.gmu.edu/stats/syllabi/inft979/GeneralizedParallelCoordinates.pdf

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 under the GNU GPL - implemented in Java

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