Relational Data Hierarchies CSC544 Why hierarchies? - - PowerPoint PPT Presentation

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Relational Data Hierarchies CSC544 Why hierarchies? - - PowerPoint PPT Presentation

Sep 23, 2022 529 likes •1.15k views

Relational Data Hierarchies CSC544 Why hierarchies? http://www.sci.utah.edu/~miriah/cs6630/lectures/L13-trees-graphs.pdf Scatterplots; dot plots; line charts, etc. Until now, our data points were independent of one another In

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Relational Data Hierarchies

CSC544

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Why hierarchies?

http://www.sci.utah.edu/~miriah/cs6630/lectures/L13-trees-graphs.pdf

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Until now, our data points were “independent of one another” Scatterplots; dot plots; line charts, etc.

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In “relational data”, it’s the relationship between points that matters

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  • The reports-to relationship in an organization
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  • The “tree of life”
  • evolution of species creates branching

mechanism and “ancestor-of” relationship

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Tree Hierarchy

  • “Rooted tree”: Every node has exactly one “parent”

node, except for the root, which has none

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What do we want our drawings to show?

  • Who reports to whom
  • … and who doesn’t
  • How big are sub-trees
  • etc
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Many different ways to visualize trees

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http://homes.cs.washington.edu/~jheer/files/zoo/ex/hierarchies/tree.html

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http://www.cs.rug.nl/svcg/SoftVis/ViewFusion

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http://jsfiddle.net/VividD/WDCpq/8/

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Reingold-Tilford binary tree drawing

  • aesthetics: properties which we believe are responsible for good drawings
  • 1) nodes at same level of tree should lie along a horizontal line
  • 2) left child should be positioned to the left of parent; same with right

child

  • 3) parent should be centered over children
  • 4) subtree drawing should be independent of subtree position on general

drawing, and tree and “its mirror” should produce mirror drawings of one another

http://hci.stanford.edu/courses/cs448b/f11/lectures/ CS448B-20111110-GraphsAndTrees.pdf

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Reingold-Tilford tree drawing

http://www.reingold.co/tidier-drawings.pdf

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Reingold-Tilford Algorithm

  • Bottom-up tree traversal
  • y-coord is the depth of the node, x-coords are “locally defined” (so

first is arbitrary)

  • merge trees
  • push right tree as close as possible to left tree (this is where the

contour comes in)

  • position shifts saved at each node
  • parent nodes are centered above direct children
  • Final top-down pass to convert shifts to positions
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Reingold-Tilford Algorithm,

  • nce again
  • Bottom-up tree traversal
  • y-coord is the depth of the node, x-coords are “locally defined” (so

first is arbitrary)

  • merge trees
  • push right tree as close as possible to left tree (this is where the

contour comes in)

  • position shifts saved at each node
  • parent nodes are centered above direct children
  • Final top-down pass to convert shifts to positions
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Bubble Charts

  • Represent hierarchy by containment
  • Let’s work out a simple algo!
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Treemaps

  • Represent hierarchy by containment,
  • … and sizes by areas
  • Let’s work out a simple algo!
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Squarified Treemaps

  • A little harder, tries to make square shapes
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Not all Hierarchies are Trees

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Given what we know about tree drawing, how do we draw a DAG?

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The evolution of UNIX

http://www.graphviz.org/Gallery/directed/unix.svg

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The evolution of UNIX

http://www.graphviz.org/Gallery/directed/unix.svg

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Directed, Acyclic Graphs

  • Like a hierarchy, but “direct ancestor” is not unique
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Let’s draw a DAG

  • Compute rank: height of node
  • Requirement: if aRb, height(a) > height(b)
  • Order nodes of same rank to minimize crossings
  • This is known as a “Sugiyama layout” for its

inventor

  • Gansner et al., A Technique for Drawing Directed
  • Graphs. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=221135
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Let’s draw a DAG

  • Gansner et al., A Technique for Drawing Directed
  • Graphs. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=221135
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Given what we know about treemaps, can we draw a DAG?

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Euler Diagrams (Venn Diagrams)

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Euler Diagrams

  • Represent relationship by

containment

  • Algorithms are very

complicated, tend to produce bad shapes

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Euler Diagrams

  • Doesn’t scale to large

diagrams

http://raweb.inria.fr/rapportsactivite/RA2009/gravite/3.png

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Euler Diagrams

  • Doesn’t scale to “large”

diagrams

64 regions 16 regions

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Recap

Not a Hierarchy Hierarchy Not a Tree NEXT Sugiyama’s algorithm Euler Diagrams A Tree NEXT Reingold-Tilford Treemaps