## Our Blog

### Better Know a Visualization: Parallel Coordinates

(With enough visualization methods to warrant a periodic table, it can be confusing to know what to use and when—and which visualizations are even worth considering at all. This series of posts is intended to introduce you to the visualization approaches that we find most useful, practical, and audience-friendly.)

#### What is a parallel coordinates chart?

Parallel coordinates is a visualization technique used to plot individual data elements across many dimensions. Each of the dimensions corresponds to a vertical axis and each data element is displayed as a series of connected points along the dimensions/axes.

Jon Peltier’s chart of baseball players below offers a simple example.

Each line corresponds to a player with performance plotted across four characteristics. Two players have been highlighted to compared values.

Parallel coordinates was invented by Alfred Inselberg in the 1970s as a way to visualize high-dimensional data. These charts are more often found in academic and scientific communities than in business and consumer data visualizations. This isn’t too surprising as parallel coordinate charts can become very dense and difficult to comprehend. Stephen Few has a typical reaction (PDF):

The first time that I saw a parallel coordinates visualization, I almost laughed out loud. My initial impression was “How absurd!” I couldn’t imagine how anyone could make sense of the dense clutter caused by hundreds of overlapping lines. This certainly isn’t a chart that you would present to the board of directors or place on your Web site for the general public. In fact, the strength of parallel coordinates isn’t in their ability to communicate some truth in the data to others, but rather in their ability to bring meaningful multivariate patterns and comparisons to light when used interactively for analysis.

Mr. Few’s final point is right on: with the application of interactive highlighting, filtering, and roll-over detail, parallel coordinate charts can reveal interesting stories in your data.

#### What problem does this solve?

For most standard charts, there are only so many dimensions you can effectively show. A typical progression of charts by dimensions goes like this:

 Dimensions Chart type 2 Scatterplot 3 Bubble chart 4 Bubble chart with colors 5 Bubble chart with colors and animation

And now you’ve pretty much made an indecipherable graphic. That’s where parallel coordinates can help in showing many dimensions, limited only by horizontal space.

Like all good visualizations, parallel coordinates can also show both the forest and the tree. The big picture can be seen in the patterns of lines; individual lines can be highlighted to see detailed performance of specific data elements.

#### What to watch out for when using parallel coordinates?

With its power to visualize multi-dimensional data, why aren’t parallel coordinate chart more popular? Here are a few of the issues:

• Large data sets create a lot of visual clutter. More from S. Few: “Most of us who have used parallel coordinates to explore and analyze multivariate data would agree that meaningful patterns can be obscured in a clutter of lines, especially with large data sets.”
• The order of the axes impacts how the reader understands the data. Relationships between adjacent dimensions are easier to perceive than between non-adjacent dimensions.
• As the axes get closer to each other it becomes more difficult to perceive structure or clusters.
• Depending on the data, each axis can have a different scale, which is difficult to display and for the reader to absorb.
• Lines may be mistaken for trends or change in values even thought they are only used to show the connected relationship of points.
• Then there is stuff like the following that can give the visualization technique a bad name:

#### Parallel coordinates in practice

Protovis: In this example, hundreds of cars can be quickly compared by filtering along any dimension. Click and drag along the red rule for a given dimension to update the filter.

Junk Charts revised a New York Times graphic to come up with this take on a parallel coordinates chart:

Advisor Solutions’s Parabox solution goes beyond the parallel coordinate lines to also show information about the distribution of values by dimension.

#### Do it yourself with other tools

• Macrofocus uses parallel coordinate visualizations extensively in their products (InfoScope, SurveyVisualizer)
• GGobi is an open source visualization program for exploring high-dimensional data”
• FluxViz is a simple cross-platform tool that uses parallel coordinates for the visualization of high-dimensional spaces”

#### More resources

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• Robert Kosara

There is a lot more to Parallel Coordinates than that. You’re right with your criticism, but you don’t show how this can be used for a lot of data sets where you want to sort through lots of dimensions to find patterns. There’s also still a dozen or so new papers every year on refinements and new things based on ParCoords (and not just the 3D nonsense you showed). There are limitations of course (just like with any other technique), but there are a lot more uses than you give the technique credit for.

Also, your last two examples don’t have much to do with Parallel Coordinates: the point is to be able to see which points on the different axes belong together. You can’t do that with these charts.

• Zach

Robert, Can you share some of the other uses you mentioned?

• Robert Kosara

I was actually planning an article for my website on that topic, I’ll let you know when it’s up … should be next week.

• Robert Kosara

Okay, this took a bit longer than expected, but here it is: http://eagereyes.org/techniques/parallel-coordinates

It’s a basic intro at this point, but I intend to write a bit more about more current work with parallel coordinates in the next month or so.

• Alfred Inselberg

I also suggest my new book (which was also praised by Stephen Hawking)

“Parallel Coordinates: Visual Multidimensional Geometry and its
Applications”
http://www.springer.com/math/cse/book/978-0-387-21507-5.

which is now available. It has an easy to read chapter on Data Mining.

As Robert points out (thanks!) there is more to ||-cs. Information
is concentrated at the crossings and there several new ways to discover complex relations (please see chapter) from their corresponding patterns. It is not just “squinting” and interacting with simplistic queries. By the way, an algorithm is emerging to trasnform massive datasets in clear patterns (multidimensional “graphs”) without display clutter.

Of course remarks are welcome