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Parallel Coordinates
by Juan C. D├╝rsteler [message n║ 201]

Parallel coordinates are an extension of the usual coordinate systems, devised to solve the problem that arises when trying to represent highly multidimensional information.  At first glance they can seem complex and even confusing but they reveal all theri potential and ease of use when combined with interactivity.
CernRootPara.gif (112168 bytes)
Parallel coordinates plot. Each dimension is represented in an axis parallel to those of the remaining dimensions. Each element (equivalent to a "point" in 2D or 3D) is depicted as a broken line joining the values it takes for every dimension. In this plot the lines are dotted which reduces occlusion to a certain extent.
: As can be seen in the CERN (Centre Europeene pour la Recherche Nucleaire) website for the ROOT Data Analysis system.
Click on the image to enlarge it.

Parallel coordinates, mainly due to Alfred Inselberg, among others, constitute  a relatively recent representation system (ca. 1981). Their objective is to solve the problem of representing multidimensional data sets.  They are based on representing each dimension as a vertical scale parallel to all the others. Each element of the data set corresponds to a zigzag line joining the specific values of each one of its variables. This is equivalent to the "point" in a 2 or 3-D representation. 

At first glance it could seem a complex and even confusing visualization, despite its high conceptual simplicity. Nevertheless an adequate use of the visual variables (colour, transparency...) and of interaction turn them into a powerful tool.

The fact that the space we are immersed in is (at least apparently) 3-dimensional makes the representation of multidimensional systems difficult. In a multidimensional system the number of variables that define each of its elements is greater than 3 --see the definition of dimension in the glossary). The representation is increasingly difficult with the higher number of dimensions.

The Cartesian representation is very easy to apprehend since it visually coincides with what we see in our 3D world. A getaway to this limitation regarding dimensions consists of using visual variables, like colour, orientation, shape of each element, etc. or adding icons to every point with the aim of increasing the information. In any case the overall 2D or 3D familiar reference is always maintained.

With such a type of scheme you can increase the represented dimensions to around ten at most. Nevertheless, many problems exhibit a dimensionality neatly superior to this figure. Overcoming this limit implies breaking with the traditional cartesian scheme and leads us to the search for visual metaphores unbound to the common concept of 2D or 3D space. 

A natural way to increase dimensionality is just by adding more axis around the origin of coordinates, which originates the star charts also known as "radar" plots. This allows you to represent some tens (at most 20-25) of dimensions before occlusion makes itself very apparent if the number of elements ("points") to represent  is not very high.

RadarAccidentes.gif (107424 bytes)
Radar (or Star) chart. You can see the overlapping and occlusion of the different results shown.
Source: Chart by the author with data from car crash statistics between 1998 and 2007 (data from Dirección General de Tráfico, Spain)
Click on the image to enlarge it

In this case an element of the dataset is represented by a polyline joining the values for each variable range, depicted as one of the axis. This generates a chart similar to a spider's web, a star or a radar display, hence its name.

Star charts  are prone to occlusion when the number of elements to be represented is high. They have the additional inconvenience that the lines closer to the origin of coordinates have a lower linear extent than those in the periphery. This makes their ink/data ratio lower than the former ones.

Parallel coordinates charts are also prone to occlusion. Nevertheless the fact that their axis are parallel provides them with some advantages over their starry cousins:

  • Irrespective to whether the values that the lines join are high or low the ink/data ratio is better balanced. The more variable the behaviour of the element, the higher this ratio will be. Conversely the more stable in behaviour the ratio, the lower the ratio will be, hence being associated to the features of the data and not to the structure of the representation.

  • More dimensions can be represented since parallel coordinates make better use of the screen or paper real estate.

  • There's no singularity (the origin) that can make the information disappear when the elements have very low values across their whole range of variables. In radar charts this happens due to┬álack of space and /or to the confusion the union of many axis near the origin generates.

But where parallel coordinates show to be more operative is when adding interactivity.  By adding the possibility to select within each dimension the range of values that we want to see, for example by adding a slider to each axis à la InfosCope makes them a powerful multidimensional selection tool.
InfoScopeBcn.gif (131018 bytes)
Infoscope, with the data from Barcelona city highlighted.
Source: Screenshot by the author.
Click on the image to enlarge it

We have talked already about InfoScope in the number 54, when the tool was still named CityO'Scope, but it still is an excellent example of what parallel coordinates and multiple coordinated views allow you to do. We strongly recommend to the interested reader to download the free application and play around with it a little.

Despite the powerful appearance these types of representations can appear confusing, with so many lines criss-crossing. What can we say about their ease of use?

Certain research studies done at the Tampere University in Finland, presented to IV'09 in the article "Visual Perception of Parallel Coordinate Visualizations" using eye-tracking and comparing the visual paths used by neophytes in the use of parallel coordinates with the optimum ones point out the following: 

  • even the most inexperienced users learn quickly to use this visual metaphor.┬á l

  • they pay attention to appropriate visualization areas according to the task they are performing.

  • they quickly become proficient in the use of parallel coordinates.

Finally there exist several toolkits that allow you to easily represent multidimensional data in the form of parallel coordinates. Among them we can cite Parvis, in its latest version (2003). Written in Java it allows you to upload a .stf file with your data and see them quickly converted into a parallel coordinates visualization you can interact with.

More recent id FluxViz (2008) , written in C, requires a compiler to convert the source code in an application and it works with simple data files. Other toolkits like VTK provide functions in C language that allow you to include parallel coordinates in your applications.

Parallel coordinates make up a technique that is still not very common. Nevertheless they are easier to learn and to use than the average user might think. Together with interaction (or maybe thanks to it) their potential is undeniable, specially when using them for the selection of the best compromises within a range ruled by a very high quantity of parameters.

Visual Perception of Parallel Coordinate Visualizations. Harri Siirtola et al. Proceedings of the 2009 13th International Conference Information Visualisation, Pages:3-9

Links of this issue:

http://root.cern.ch/root/Version517.news.html   Web page of the ROOT system at CERN
http://www.math.tau.ac.il/~aiisreal/   Alfred Inselberg web page
http://www.infovis.net/printRec.php?rec=glosario&lang=2#Dimension   Glossary entry: Dimension
http://www.macrofocus.com/public/products/infoscope/   Infoscope by Macrofocus
http://www.infovis.net/printMag.php?num=54&lang=2   Number 54 about City'O'Scope
http://www.mediavirus.org/parvis/documentation.html   Parvis web page
http://sourceforge.net/projects/fluxviz/   Fluxviz web page
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