A Quick Overview of Some Visualization Techniques and

Suggestions for Projects

Prof. Michael McGuffin

ETS, Montreal, Canada

http://profs.logti.etsmtl.ca/mmcguffin/

There are two main kinds of data we can visualize:

multidimensional data (which includes tables, mathematical

relations, and functions),and network data

(which includes trees).

Multidimensional Data:Scatterplot Matrices

Multidimensional Data

Consider students’ marks in …• Physics: 90%• Math: 95%• French Literature: 65%• History: 70%

Each student can be thought of as a tuple• (90%, 95%, 65%, 70%)• Etc.

Scatterplot Matrix (SPLOM)

Physics

Math

FrenchLiterature

History

(90%, 95%, 65%, 70%)

FrenchLiterature

Math

Scatterplot Matrix (SPLOM)

Physics

Math

FrenchLiterature

History

(90%, 95%, 65%, 70%)

(30%, 20%, 90%, 90%)

FrenchLiterature

Math

Scatterplot Matrix (SPLOM)

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Within each scatterplot, we could be interested in seeing outliers, correlations, etc.

Notice: the upper triangular half is the same as the lower triangular half, and the diagonal is not very interesting.

Scatterplot Matrix (SPLOM)

Wilkinson, Anand, Grossman,“Graph-Theoretic Scagnostics”, 2005

Notice: the diagonal is used to show the names of dimensions.

Example from Matlab: “carbig.mat”

http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/mvplotdemo.html

SPLOM with histograms along the diagonal. Colors indicate the number of cylinders in the engine of each automobile.

Matrix of correlation coefficientsWhen we have many dimensions, we can summarize each scatterplot by computing its correlation coefficient and displaying only that, instead of

displaying all the individual data points. The below interface also allows the user to select one scatterplot and see a zoomed-in view for details.

Jinwook Seo and Ben Shneiderman, “A Rank-by-Feature Framework for …”, Proceedings of InfoVis 2004.

Corrgrams (Michael Friendly, 2002)

http://www.math.yorku.ca/SCS/Gallery/images/corrgram2t.gif

Multidimensional Data:Parallel Coordinates

(Alfred Inselberg and others)

Multidimensional Data

Consider students’ marks in …• Physics: 90%• Math: 95%• French Literature: 65%• History: 70%

Each student can be thought of as a tuple• (90%, 95%, 65%, 70%)• Etc.

Parallel Coordinates

100%

0%

Physics MathFrenchLiterature History

(90%, 95%, 65%, 70%)

Parallel Coordinates

100%

0%

Physics MathFrenchLiterature History

(90%, 95%, 65%, 70%)

(30%, 20%, 90%, 90%)

Parallel Coordinates

Johansson et al. 2005

Parallel Coordinates

Ellis, Bertini, Dix, “The Sampling Lens …”, 2005Ellis, Dix, “Enabling Automatic Clutter Reduction …”, 2006

Multidimensional Data:Scatterplot and Parallel Coordinate

Combinations

Example from Matlab: “carbig.mat”

http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/mvplotdemo.html

[Lopez, McGuffin, & Barford; not yet published]

Combinations of Parallel Coordinates and Scatterplots

Steed et al. 2009 Holten and van Wijk 2010

Yuan et al. 2009

Multidimensional Data:Glyphs

The fonction y = x^0.5:

x y--- --- 0 0 1 1 4 2 9 3...

The relation in a table of a relational database:

Client_name Product_purchased Price Date ...------------- ----------------- ------- ------------ -----Robert G. Trombone 500.00 2008 mars 7 .Robert G. Partitions vol. 1 45.00 2008 mars 7 .Lucie M. Flute 180.00 2007 nov 11 .Cynthia S. Partitions vol. 2 40.00 2008 juin 16Jules T. Piano 6000.00 2008 jan 10Jules T. Partitions vol. 1 45.00 2008 jan 13...

A video (for example, an .avi file):

x y time red green blue--- --- ------- ------- ------ ------ 0 0 0 255 0 0 0 1 0 200 10 6 ... 0 0 0.1 255 50 100 0 1 0.1 255 200 190 ...

Examples of relations. A relationis a subset of a cartesian product of two or more sets. Each relation can be thought of as a multidimensional data set. In the examples here, each row is a tuple, each column is a dimension.

Chernoff faces (1973)(an example of a "glyph")

Advantage: better than text to get a global impression of the data and to find interesting elements.

Disadvantage: the mapping from variables to faces has an effect on the saliency of each variable.

Disadvantage(?): redundancy of a symmetrical face.

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Other examples of glyphs

M. Ward (2002), “A Taxonomy of Glyph Placement Strategies for Multidimensional Data Visualization”, Information Visualization.

Interactive Presentation from the U.N.(United Nations Development Programme, Human Development Report)

See also Hans Rosling’s presentation on http://www.ted.com

Notice: the points are glyphs!

Multidimensional Data:Other techniques …

The fonction y = x^0.5:

x y--- --- 0 0 1 1 4 2 9 3...

The relation in a table of a relational database:

Client_name Product_purchased Price Date ...------------- ----------------- ------- ------------ -----Robert G. Trombone 500.00 2008 mars 7 .Robert G. Partitions vol. 1 45.00 2008 mars 7 .Lucie M. Flute 180.00 2007 nov 11 .Cynthia S. Partitions vol. 2 40.00 2008 juin 16Jules T. Piano 6000.00 2008 jan 10Jules T. Partitions vol. 1 45.00 2008 jan 13...

A video (for example, an .avi file):

x y time red green blue--- --- ------- ------- ------ ------ 0 0 0 255 0 0 0 1 0 200 10 6 ... 0 0 0.1 255 50 100 0 1 0.1 255 200 190 ...

Examples of relations. A relationis a subset of a cartesian product of two or more sets. Each relation can be thought of as a multidimensional data set. In the examples here, each row is a tuple, each column is a dimension.

Red

Blue

Green

A video

Network Data:Node-Link Diagrams

Note: in the context of this discussion, the word “graph” means the same thing as “network”, i.e., a “graph” is a topological structure with nodes and edges that can be drawn many different ways. In more

general English conversation, however, the word “graph” may simply mean a picture showing a mathematical function or something similar. To avoid confusion, it is often good to use the word “network” to refer to

the topological structure.

Generated with a “SugiyamaLayout”( http://www.ogdf.net/ogdf.php/tech:howto:hierlr )

Generated by Graphviz( http://www.graphviz.org/Gallery/directed/unix.html )

How to compute the layout of a graph?

• Many algorithms are available– See “Graph Drawing” annual conference proceedings– See book “Graph Drawing: Algorithms for the Visualization

of Graphs” by Di Battista et al. (1999)– Examples: Reingold-Tilford (1981) for binary trees,

Sugiyama et al. (1981) for directed acyclic graphs (DAGs), or examples on previous slide

• Most of these algorithms are not easy to implement• One class of algorithms that are easy to implement

(in their naïve form) and that are applicable to any graph: force-directed layout

Force-Directed Layout of a Network in 3D

http://profs.logti.etsmtl.ca/mmcguffin/research/graph3D/

•Pseudo-physical simulation of masses and springs that converges toward a final layout

•The nodes are masses that are mutually repelled by an electric force

•The edges are springs

Tree Data

A tree can be thought of as simply a special kind of network.

A naïve and easy-to-program layout: each subtree has an interval in x that is not overlapped by the neighboring subtrees. A postorder depth-first-traversal combines the intervals of subtrees to yield the interval of a parent node.

A "Reingold Tilford" style layout : saves space in x by moving subtrees together as much as possible. (For details, see section 3 of Christoph Buchheim, Michael Jünger and Sebastian Leipert, "Improving Walker's Algorithm to Run in Linear Time", Proceedings of Symposium on Graph Drawing (GD) 2002, pages 344-353.) The is more complicated to program.

Another easy-to-program layout: a preorder depth-first-traversal encounters nodes in order of their y coordinates, and the x coordinate of each node is proportional to its depth.

Classical/Layered Indented Outline List

A naïve and easy-to-program layout: each subtree has an interval in x that is not overlapped by the neighboring subtrees. A postorder depth-first-traversal combines the intervals of subtrees to yield the interval of a parent node.

A "Reingold Tilford" style layout : saves space in x by moving subtrees together as much as possible. (For details, see section 3 of Christoph Buchheim, Michael Jünger and Sebastian Leipert, "Improving Walker's Algorithm to Run in Linear Time", Proceedings of Symposium on Graph Drawing (GD) 2002, pages 344-353.) The is more complicated to program.

Another easy-to-program layout: a preorder depth-first-traversal encounters nodes in order of their y coordinates, and the x coordinate of each node is proportional to its depth.

Classical/Layered Indented Outline List

A naïve and easy-to-program layout: each subtree has an interval in x that is not overlapped by the neighboring subtrees. A postorder depth-first-traversal combines the intervals of subtrees to yield the interval of a parent node.

A "Reingold Tilford" style layout : saves space in x by moving subtrees together as much as possible. (For details, see section 3 of Christoph Buchheim, Michael Jünger and Sebastian Leipert, "Improving Walker's Algorithm to Run in Linear Time", Proceedings of Symposium on Graph Drawing (GD) 2002, pages 344-353.) The is more complicated to program.

Another easy-to-program layout: a preorder depth-first-traversal encounters nodes in order of their y coordinates, and the x coordinate of each node is proportional to its depth.

Classical/Layered Indented Outline List

Trees

Michael McGuffin and Jean-Marc Robert, 2010

Trees

Treemaps(Ben Shneiderman and others)

http://www.cs.umd.edu/hcil/treemap-history/

Martin Wattenberg, 1998and

http://www.smartmoney.com/marketmap/

Marc Smith and Andrew Fiore, 2001

Focus+Context Visualizations

Fisheye lens

Image: Keahey and Robertson

3D Visualizations

3D + interaction + animations :Christopher Collins and Sheelagh Carpendale, 2007

Project Ideas on the Wiki

Possible project topics:• visualization of multidimensional data (using parallel coordinates,

using scatterplot matrix, using glyphs,...) Example data sets:– http://archive.ics.uci.edu/ml/datasets/Iris– http://vis.stanford.edu/protovis/ex/cars.html– http://vis.stanford.edu/protovis/ex/flowers.html

• visualization of one tree (genealogy tree, evolutionary tree, files on harddrive,...)– Example: http://www.cs.umd.edu/hcil/treemap-history/

• visualization of differences between two trees• visualization of one network (using node-link diagram, using

adjacency matrix,...)• visualization of differences between two networks• visualization of time series data

Example: http://leebyron.com/else/streamgraph/• a 3D visualization• a zoomable user interface

Some libraries, APIs, software, and platforms:• InfoVis Toolkit (Java) http://ivtk.sourceforge.net/• Prefuse (Java) http://prefuse.org/• Flare (ActionScript) http://flare.prefuse.org/• Protovis (JavaScript) http://vis.stanford.edu/protovis/ http://eagereyes.org/tutorials/protovis-primer-part-1• Many Eyes http://manyeyes.alphaworks.ibm.com/• VTK (C++ / Java / Python) http://vtk.org/• Processing (Java) http://processing.org

For visualizing networks• Pajek http://pajek.imfm.si/• Graphviz http://www.graphviz.org/• Tulip http://www.tulip-software.org/• Walrus http://www.caida.org/tools/visualization/walrus/• JUNG http://jung.sourceforge.net/• NetworkX (Python) http://networkx.lanl.gov/

For multidimensional data• XmdvTool http://davis.wpi.edu/~xmdv/• Spotfire http://www.cs.umd.edu/hcil/spotfire/• Polaris http://window.stanford.edu/projects/polaris/• Tableau http://www.tableausoftware.com• Mondrian http://rosuda.org/Mondrian

Some websites and blogs:• http://infosthetics.com• http://flowingdata.com• http://eagereyes.org• http://www.visualcomplexity.com/vc/blog/• http://manyeyes.alphaworks.ibm.com/blog/• http://www.gapminder.org/

Some Books about Visualization• Jacques Bertin (1967), Sémiologie graphique: Les diagrammes, Les réseaux, Les

cartes.• Jacques Bertin (1977), La graphique et le traitement graphique de l'information.• John Wilder Tukey (1977), Exploratory Data Analysis.• Edward R. Tufte (1983), The Visual Display of Quantitative Information.• Edward R. Tufte (1990), Envisioning Information.• Edward R. Tufte (1997), Visual Explanations: Images and Quantities, Evidence and

Narrative.• Di Battista, Giuseppe and Peter Eades and Roberto Tamassia and Ioannis G. Tollis

(1999), Graph Drawing: Algorithms for the Visualization of Graphs.• Leland Wilkinson (1999), The Grammar of Graphics.• Stuart K. Card and Jock D. Mackinlay and Ben Shneiderman (1999), Readings in

Information Visualization: Using Vision to Think.• Colin Ware (2000), Information Visualization: Perception for Design.• Robert Spence (2001), Information Visualization.

A bibliography of books and papers

http://profs.logti.etsmtl.ca/mmcguffin/bib/vis.txt