Transcript Overview and Detail

Hierarchies and Trees 1
CS 7450 - Information Visualization
March 8, 2005
John Stasko
Hierarchies
• Definition
 Data repository in which cases are related to
subcases
 Can be thought of as imposing an ordering in
which cases are parents or ancestors of other
cases
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Hierarchies in the World
• Pervasive
 Family histories, ancestries
 File/directory systems on computers
 Organization charts
 Animal kingdom: Phylum,…, genus,…
 Object-oriented software classes
 ...
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Trees
• Hierarchies often represented as trees
 Directed, acyclic graph
• Two main representation schemes
 Node-link (today)
 Space-filling
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Node-Link Diagrams
• Root at top, leaves at bottom is very
common
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Sample Representation
Johnson & Shneiderman, ‘91
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Examples
Good for?
Search
Bad for?
Understanding
structure
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Why Put Root at Top?
Root can be at
center with levels
growing outward
too
Can any node
be the root?
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Drawing a Tree
How does one draw this?
• DFS
• Percolate requirements upward
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Potential Problems
• For top-down, width of fan-out uses up
horizontal real estate very quickly
 At level n, there are 2n nodes
• Tree might grow a lot along one particular
branch
 Hard to draw it well in view without knowing
how it will branch
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InfoVis Solutions
• Techniques developed in Information
Visualization largely try to assist the
problems identified in the last slide
• Alternatively, Information Visualization
techniques attempt to show more
attributes of data cases in hierarchy or
focus on particular applications of trees
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3D Approaches
• Add a third dimension into which layout
can go
• Compromise of top-down and centered
techniques mentioned earlier
• Children of a node are laid out in a
cylinder “below” the parent
 Siblings live in one of the 2D planes
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Cone Trees
Developed at
Xerox PARC
3D views of
hierarchies
such as file
systems
Robertson, Mackinlay, Card
CHI ‘91
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Video
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Alternate Views
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Cone Trees
• Positives & negatives?
 Discuss
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Cone Trees
• Positive
• Negative
 More effective area to
lay out tree
 Use of smooth
animation to help
person track updates
 Aesthetically pleasing
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 As in all 3D, occlusion
obscures some nodes
 Non-trivial to
implement and
requires some
graphics horsepower
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Alternative Solutions
• Change the geometry
• Apply a hyperbolic transformation to the
space
• Root is at center, subordinates around
• Apply idea recursively, distance decreases
between parent and child as you move
farther from center, children go in wedge
rather than circle
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Hyperbolic Browser
• Focus + Context Technique
 Detailed view blended with a global view
• First lay out the hierarchy on the
hyperbolic plane
• Then map this plane to a disk
• Start with the tree’s root at the center
• Use animation to navigate along this
representation of the plane
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Lamping and Rao,
JVLC ‘96
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2D Hyperbolic Browser
• Approach:
Lay out the
hierarchy on the hyperbolic
plane and map this plane onto a
display region.
• Comparison
 A standard 2D browser: 100
nodes (w/3 character text
strings)
 Hyperbolic browser: 1000
nodes, about 50 nearest the
focus can show from 3 to
dozens of characters
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1
2
3
Clicking on the blue
node brings it into
focus at the center
4
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Watch it Work
• Video
• Demo from Inxight web site
• Live demo from laptop showing file
system
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Key Attributes
• Natural magnification (fisheye) in center
• Layout depends only on 2-3 generations
from current node
• Smooth animation for change in focus
• Don’t draw objects when far enough from
root (simplify rendering)
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Problems
• What might be problems with this
approach?
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Problems
• Orientation
 Watching the view can be disorienting
 When a node is moved, its children don’t
keep their relative orientation to it as in
Euclidean plane, they rotate
 Not as symmetric and regular as Euclidean
techniques, two important attributes in
aesthetics
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How about 3D?
• Can same hyperbolic transformation be
applied, but now use 3D space?
• Sure can
• Have fun with the math!
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H3Viewer
Munzner,
IEEE CG&A ‘98
Video
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Layout
• Find a spanning tree from an input graph
 Use domain-specific knowledge
• Layout algorithm
 Nodes are laid out on the surface of a
hemisphere
 A bottom-up pass to estimate the radius
needed for each hemisphere
 A top-down pass to place each child node on
its parental hemisphere’s surface
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Drawing
• Maintain a target frame by showing less of
the context surrounding the node of
interest during interactive browsing
• Fill in more of the surrounding scene
when the user is idle
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Navigation
Translation of a node to the center
Rotation around the same node
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Performance
• Handle much larger graphs, i.e. >100,000
edges
• Support dynamic exploration & interactive
browsing
• Maintain a guaranteed frame rate
http://graphics.stanford.edu/~munzner/
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See the Forest...
• How about collections of trees? (Forests)
• Multitrees (M-trees)
 “A class of directed acyclic graphs (DAGs)…
(that) have large easily identifiable
substructures that are trees.”
 M-trees are DAGs, not trees, but…
Furnas & Zacks,
CHI ‘94
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Multitrees are DAGs
• Can be built by adding new tree structure
above existing subtrees
• The descendants of any node form a tree
of contents
• The ancestors of any node form a tree of
contexts
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Example
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Composition
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Old School
• After all the interest in 3D and hyperbolic
techniques in the ’90’s, recently, there has
been renewed interest in the old 2D
methods (just done better)
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Degree-of-Interest Trees
• Uses traditional 2D techniques with
additions:
 Drawing based on estimation of user’s DOI
 Elision of nodes with low DOI
 Geometric scaling of node size based on DOI
 Semantic scaling of node contents with size
 Clustered representations of large,
unexpanded branches
 Smooth animated focus transitions
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Card & Nation
AVI ‘02
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Example Operations
1. Display of a uniform tree of 4 levels
2. Same table with focus on Node 3
3. Same tree expanded down to a leaf node
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Useful Contents
Organization chart with over 400 nodes accessible over WWW through Web browser
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SpaceTree
• Uses conventional 2D layout techniques
• Adds:
 Dynamic rescaling of branches for better
space use
 Smart camera movements
 Preview icons for branch topologies
Grosjean, Plaisant, Bederson
InfoVis ‘02
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SpaceTree Example
Video
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Polyarchy Visualization
• Visualizing multiple intersecting
hierarchies
• Developed some
visual transition
techniques
including animation
Robertson, Cameron, Czerwinski, & Robbins
CHI ’02, InfoVis Journal ‘02
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Food for Thought
• Which of these techniques are useful for
what purpose?
• How well do they scale?
• What if we want to portray more variables
of each case?
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HW 6
• Due a week from today
• Thursday’s lecture may help
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Project
• Be working on design ideas
• Mid-term report due next Thursday
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Upcoming
• Trees 2 - Space-filling tree representations
 Reading
Chapter 8
Johnson & Shneiderman
• Text & documents
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References
• Spence and CMS texts
• All referred to papers
• Cai & Krohne and Pan & Wang F ‘99 slides
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Extra Slides
• Multitrees
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No Diamonds
• Diamonds are not
permitted
• Occurs when there
are 2 distinct directed
paths between 2
nodes.
• At most one directed
path between 2
nodes.
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Centrifugal View
• A view of the ancestors (context) and
descendants (children) of an individual
(interior) node
• Transitions between centrifugal views can
be animated
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Centrifugal View
Directions
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Contents Fisheye View
• Downward tree of contents rooted at the
context “User JMZ”
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Contexts Fisheye View
• Inverted tree of contexts rooted at the content
“Directions”
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Integrated Fisheye View
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