Marti Hearst

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SIMS 247 Lecture 10More on Distortion-based
ViewsHow many ways to show a graph?

• February 19, 1998

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Today

• More on distortion techniques
• Perspective Wall
• Document Lens
• Hyperbolic Browser
• How many ways can we view a graph?

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Distortion Techniques

• Computation must take care not to let the
  magnified part overlap or cover up the
  de-magnified part
• Must consider the boundary between the magnified
  and the demagnified
• Some techniques have an abrupt boundary
• Some are more gradual

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Perspective Wall (Mackinlay et al 91)

• Idea
• focus on a subpart of a table
• show the rest of the table in the periphery
• Goal
• help user retain an understanding of the context
  of the part of the table they are focusing on

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Perspective Wall (Mackinlay et al. 91)
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Document Lens (Robertson Mackinlay 93)

• Goal show a long document in context
• Approach
• lay pages out in a grid (on a table)
• focus view on one page
• show rest of pages distorted into a pyramid-like
  layout
• use greeking and other techniques to simply
  suggest what is on the other pages

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How many ways can we view a graph?

• Expand/contract hierarchy
• like a mac or windows file browser
• Hyperbolic tree browser
• Layout via dynamic arrangement
• 2D/3D force-directed placement
• Simulated annealing
• Cluster tree hierarchies
• Multitrees
• Cone Trees
• Treemaps

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Dynamic Grouping and Clustering

• Start with an initial (random) organization
• Apply a function to change the layout
• Repeat until some stopping condition is reached
• Two common techniques
• nodes and springs
• aka attraction and repulsion forces
• aka force-directed placement
• simulated annealing

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Force-Directed Placement(Fruchterman Rheingold
90)

• Also called attraction and repulsion and
  nodes-and-springs
• Works well on sparse graphs
• Edges modeled as springs that cause the vertices
  on either end to be attracted to each other
• Vertices are repulsive forces
• The repulsive forces balance the attractive
  forces to keep vertices from ending up too close
  together
• The procedure iterates
• start with random placement
• compute attraction/repulsion
• do a new layout
• repeat until some stopping threshold is met

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Force-Directed Placement(Amir 93, based on
Fruchterman and Rheingold 90)
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Force-Directed Placement(Amir 93, based on
Fruchterman and Rheingold 90)
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Force-Directed Placement(Amir 93, based on
Fruchterman and Rheingold 90)
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Attraction and Repulsion Forces(Amir 93, based
on Fruchterman and Rheingold)
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Computing Layout

• The procedure iterates
• start with random placement
• compute attraction/repulsion
• do a new layout
• repeat until some stopping threshold is met
• Given two vertices v1 and v2
• Distance between v1 and v2 is x

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3D Force-Directed Placement

• Hendley et al. paper shows 3D versions of
  force-directed placement
• They also group close-together nodes into
  super-nodes

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Hyperbolic Browser

• Focus Context Technique
• detailed view blended with a global view
• First lay out the hierarchy on Poincare mapping
  of the hyperbolic plane
• Then map this plane to a disk
• Use animation to navigate along this
  representation of the plane
• Start with the trees root at the center

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Hyperbolic Browser

• In the hyperbolic plance, the circumference and
  area of a circle grow exponentially with its
  radius
• Allocate each node a wedge of the hyperbolic
  plane
• The node recursively places all its children
  within an arc of that wedge
• at an equal distance from itself
• far enough out so the children are separated by
  at least a minimum distance
• Parallel lines diverge in hyperbolic geometry
• each childs wedge will span about the same angle
  as its parents
• but not childrens wedges will overlap

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Hyperbolic Tree Browser (Lamping et al. 95)
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Cluster Graphs (Eades and Qingwen 96)

• Simulated annealing and nodes-and-springs create
  ball-like structures
• Alternative draw tree in three dimensions
• put each level of the hierarchy on a different
  plane
• have tree-like properties between planes
• have graph-like properties within planes

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Cluster-graphs (Eades Qingwen 96)
tree-like between planes
graph-like within planes
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Cluster-graphs (Eades Qingwen 96)
two views of convex segmentation
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Cluster-graphs (Eades Qingwen 96)
two views of rectangular segmentation
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Cone-Trees (Robertson et al. 91)

• Lay tree out onto a multi-level cone
• Use animation psuedo-3D to deal with occlusion
• Use animation to grow and shrink subparts of the
  tree

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ConeTrees (Robertson et al. 91)
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ConeTrees (Robertson et al. 91)
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Hyperbolic ConeTrees (Munzner et al. 96)Use
more of the surface than standard cone trees
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Hyperbolic ConeTrees (Munzner et al. 96)
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Multi-Trees (Furnas Zachs 94)

• Often we want more than one view on a tree
• Multi-trees convert the view of a dag (directed
  acyclic graph) into a set of overlapping trees

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TreeMapsRepresent a hierarchy as boxes of
boxes(Shneiderman others )
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To Think About

• Are there other ways to show trees and graphs?
• Which of these are useful for what purposes?
• What is the role of animation/interaction?
• How well do they work in conjunction with labels?
• How well do they scale?