Overview of Data Visualization 2

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2. Visualization & Graph Drawing
   9 October 2012
   Martin B. Smith
   martin@mbs3.org
   

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4. Visualization?
   • Practically any technique using images or
   diagrams for communication
   • Not new – cartography is old
   • Not old – computer graphics are young
   • Wide applications: architecture, product
   design, education, communication
   • A Periodic Table of Visualization Methods
   

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16. From social structure, to data, to
    visualization
    • People & relationships as data
    • Mathematical graphs as social networks
    • Network analysis as applied graph theory
    

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17. Side note: ‘Storage’ is important
    • Consider advantages and disadvantages
    of particular data structures:
    – Typically breaks down into lists and matrices
    – Incidence (edge) and Adjacency (vertex)
    • Rank algorithms by how well they:
    – Enumerate nodes, test adjacency, etc
    

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18. Graph theory – Graph drawing
    • Leonhard Euler, functions, f(x), e, i, Σ, and
    Seven Bridges of Königsberg, Prussia
    

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20. Graph layout
    • Hierarchical – source to sink
    • Tree – roots without cycles
    • Symmetric – create visual symmetry
    • Orthogonal – min. area & edge crossing
    • Spectral – eigenvectors of a matrix
    • Force/MDS – springs and electric charges
    

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24. Evaluating graph drawings
    • Is it fast to compute? Can we parallelize it?
    • Does the algorithm converge? How quickly?
    • Does it show obvious symmetries?
    • Can we adapt it with parameters?
    • Does it minimize edge crossings? Size?
    • Does vertex nearness reflect adjacency?
    • Are sizes, distances and shapes distributed
    uniformly?
    • Election 2008 visualization – let’s evaluate
    

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26. Force-directed algorithms
    • Attractive and repulsive forces simulated
    as a physical system
    • Forces can be gravity (Newton), springs
    (Hooke), charged particles (Coulomb),
    magnetism (Maxwell?)
    • Advantages: quality, flexibility, interactivity
    • Disadvantages: can be slow, hurt by local
    minima or initial conditions
    

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29. Two common force-directed algorithms
    • Fruchterman-Reingold: Nodes as steel
    rings, edges as springs, electrical
    repulsive force, step width using a global
    cooling temperature definition
    • Kamada-Kawai: Same as above, but
    instead of a temperature, minimize force
    equations with some initial node criteria
    

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31. What can we do to make graph
    drawing better for social networks?
    • Modify the graph, improve data collection
    • Add constraints to force-directed algorithm
    • Get better initial conditions, more iterations
    • Deal with orientations and coordinate systems
    • 3D -> 2D, or use more interesting forces
    • Apply multiple layout algorithms
    • Curved lines and uniform distributions
    • Come up with better algorithms in general
    

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34. EgoNet (egonet.sf.net)
    • Java, Swing – hosted at SourceForge
    • Java Universal Network/Graph Framework
    • Currently defaults to F-R, but places
    isolates regularly instead of randomly
    • We’d like to explore other optimizations
    

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36. Thank you!
    • Slides will posted (where?)
    • Martin Smith – martin@mbs3.org
    • EgoNet: http://egonet.sf.net/
    • JUNG: http://jung.sourceforge.net/
    

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38. References
    • 1. Freeman, L., Visualizing Social Networks. Journal of Social Structure
    1(1), Carnegie-Mellon, 2000.
    • 2. Giuseppe Di Battista, Peter Eades, Roberto Tamassia, Ioannis G. Tollis.
    Algorithms for Drawing Graphs: an Annotated Bibliography. Computational
    Geometry: Theory and Applications 4:235-282, 1994.
    • 3. Tamassia, R. Advances in the Theory and Practice of Graph Drawing.
    Theoretical Computer Science 217 (2), 1999.
    • 4. Fruchterman, T. M. J., & Reingold, E. M. Graph Drawing by Force-
    Directed Placement. Software: Practice and Experience, 21(11), 1991.
    • 5. Kamada, T. & Kawai, S. (1989). An algorithm for drawing general
    undirected graphs. Information Processing Letters, 31, 7-15.
    • 6. Network Workbench Community Wiki at
    https://nwb.slis.indiana.edu/community/?n=VisualizeData.HomePage
    

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