In mathematics, Parallel coordinates[1] 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.
History
In 1990, the parallel coordinate plot (PCP) was introduced as a method for visualizing multivariate data Wegman (1990).Since that time, the technique has become an important tool for those who attempt exploratory data analysis and visual data mining.
Higher dimensions
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. It is worth noting that the PCP is developed based on the projective geometry view point.
Generalized Parallel Coordinate Plot
Generalized Parallel Coordinate Plot (GPCP) Moustafa and Wegman (2001) is a more recent 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 is 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 crossing the parallel axes in the parameter space. If the interpolation function is 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 smooth, continuous on the axes, and orthogonal to each parallel axis. 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 a quick interpretation of the outcome.
References
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A. Inselberg, B. Dimsdale (1990). "Parallel coordinates: A tool for visualizing multi-dimensional geometry". In Proc. Visualization 90. San Francisco, CA: pages 361–370.
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External links
- Alfred Inselberg's Homepage, with Visual Tutorial, History, Selected Publications and Applications
- A small, easy introduction by Christopher V. Jones
- An Investigation of Methods for Visualising Highly Multivariate Datasets by C.Brunsdon, A.S.Fotheringham & M.E.Charlton, University of Newcastle, UK
- Parallel Coordinates Visualization Applet
- Using Curves to Enhance Parallel Coordinate Visualisations by Martin Graham & Jessie Kennedy, Napier University, Edinburgh, UK
- On Some Generalization of Parallel Coordinate Plots by Rida E. A. Moustafa and Edward J. Wegman, George Mason University, Fairfax, VA
- Data Loom — a parallel coordinates visualisation tool for the Mac
- parvis — a parallel coordinates tool licensed under the GNU GPL - implemented in Java