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A Quick Overview of Some Visualization Techniques and Suggestions for Projects Prof. Michael McGuffin ETS, Montreal, Canada http://profs.logti.etsmtl.ca/mmcguffin/

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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).

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Multidimensional Data: Scatterplot Matrices

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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.

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Scatterplot Matrix (SPLOM) Physics Math French Literature History (90%, 95%, 65%, 70%) French Literature Math

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Scatterplot Matrix (SPLOM) Physics Math French Literature History (90%, 95%, 65%, 70%) (30%, 20%, 90%, 90%) French Literature Math

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Scatterplot Matrix (SPLOM) Niklas Elmqvist, Pierre Dragicevic, Jean-Daniel Fekete (2008). “Rolling the Dice: Multidimensional Visual Exploration using Scatterplot Matrix Navigation”. Proceedings of InfoVis 2008. 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.

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Scatterplot Matrix (SPLOM) Wilkinson, Anand, Grossman, “Graph-Theoretic Scagnostics”, 2005 Notice: the diagonal is used to show the names of dimensions.

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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.

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Matrix of correlation coefficients When 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.

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Corrgrams (Michael Friendly, 2002) http://www.math.yorku.ca/SCS/Gallery/images/corrgram2t.gif

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Multidimensional Data: Parallel Coordinates (Alfred Inselberg and others)

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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.

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Parallel Coordinates 100% 0% PhysicsMath French Literature History (90%, 95%, 65%, 70%)

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Parallel Coordinates 100% 0% PhysicsMath French Literature History (90%, 95%, 65%, 70%) (30%, 20%, 90%, 90%)

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Parallel Coordinates Johansson et al. 2005

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

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Multidimensional Data: Scatterplot and Parallel Coordinate Combinations

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Example from Matlab: “carbig.mat” http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/mvplotdemo.html

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

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Combinations of Parallel Coordinates and Scatterplots Steed et al. 2009Holten and van Wijk 2010 Yuan et al. 2009

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Multidimensional Data: Glyphs

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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 16 Jules T. Piano 6000.00 2008 jan 10 Jules 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 relation is 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.

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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. http://kspark.kaist.ac.kr/Human%20Engineering.files/Chernoff/life_in_LA.jpg http://mapmaker.rutgers.edu/355/Chernoff_face.gif

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

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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!

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Multidimensional Data: Other techniques …

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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 16 Jules T. Piano 6000.00 2008 jan 10 Jules 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 relation is 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.

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Red Blue Green A video

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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.

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Generated with a “SugiyamaLayout” ( http://www.ogdf.net/ogdf.php/tech:howto:hierlr ) Generated by Graphviz ( http://www.graphviz.org/Gallery/directed/unix.html )

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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

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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

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

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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

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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

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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

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Trees Michael McGuffin and Jean-Marc Robert, 2010

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Trees

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Treemaps (Ben Shneiderman and others) http://www.cs.umd.edu/hcil/treemap-history/ Martin Wattenberg, 1998 and http://www.smartmoney.com/marketmap/ Marc Smith and Andrew Fiore, 2001

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Focus+Context Visualizations

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Fisheye lens Image: Keahey and Robertson

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3D Visualizations

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

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Project Ideas on the Wiki

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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

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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/

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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.

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A bibliography of books and papers http://profs.logti.etsmtl.ca/mmcguffin/bib/vis.txt

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