1. Visualization Taxonomies and Techniques Trees and Graphs
University of Texas – Pan American
CSCI 6361, Spring 2014

2. Tonight: More about Taxonomies and Techniques VTK Project
Tree and Graphs
VTK
More about visualization pipeline
Big picture last time details now
Project
Alternatives to vtk – for class and project – e.g., D3
One of many tools for creating visualizations

3. Orienting …
Card et al. reading (2nd part of chapter 1 of Information Visualization) provides detail about mapping data to visual form
E.g., different types of data
Tonight, trees (hierarchies) and graphs (networks)

4. Visualization Pipeline: Mapping Data to Visual Form (Card et al
Visualization Pipeline: Mapping Data to Visual Form (Card et al., North)
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Review and where we will focus tonight
Reading for last time and this time, (2nd part of Card et al. Chapter 1 in Information Visualization (edited book) provides detail of pipeline reference model

5. Visualization Pipeline: Mapping Data to Visual Form (Card et al
Visualization Pipeline: Mapping Data to Visual Form (Card et al., North)
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Visualizations (a bit fancier definition):
“adjustable mappings from data to visual form to human perceiver”
Series of data transformations ( )
Multiple chained transformations
Human adjusts the transformations
Entire pipeline comprises an information visualization

6. Visualization Pipeline: Visualization Stages
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Data transformations:
Map raw data (idiosynchratic form) into data tables (relational descriptions including metatags)
Visual Mappings:
Transform data tables into visual structures that combine spatial substrates, marks, and graphical properties
View Transformations:
Create views of the Visual Structures by specifying graphical parameters such as position, scaling, and clipping

7. Visualization Pipeline: Information Structure
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Visual mapping is starting point for visualization design visual form
Includes identifying underlying structure in data, and for display
Tabular structure
Spatial and temporal structure
Trees, networks, and graphs
Text and document collection structure
Combining multiple strategies
Impacts how user thinks about problem - Mental model

8. Visualization Pipeline: Tonight
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Visual mapping is starting point for visualization design visual form
Includes identifying underlying structure in data, and for display
Tabular structure
Spatial and temporal structure
Trees, networks, and graphs …
Impacts how user thinks about problem - Mental model

9. Visualization Pipeline: Some Detail
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Shneiderman’s “Data Type x Task” taxonomy only in terms of data to be displayed (Dataset)
E.g., 1D, 2D, 3D, n-dimensions
Card et al. model splits out “Visual Form”, after “Visual Mapping”
So, e.g., 3D (or n-D) data can be displayed in 2D space (dimensionality reduction)

10. Trees, Networks and Graphs
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Tree, or hierarchy, data:
Cases are related to subcases
Will consider both dataset and visual form (more later)
Tree data can be thought of as imposing an ordering in which cases are parents or ancestors of other cases
Tree is a graph = set of V, E
Root (top), leaves (bottom), parents, children

11. Trees, Hierarchies About
Pervasive
Family histories, ancestries
File/directory systems
Organization charts
Animal kingdom:
Phylum,…, genus,… , species
Object-oriented software classes …
Tree is graph = set of V, E
Root (top), leaves (bottom), parents, children
Vertex, node, “item”
Entity, element
E.g., office / person
Edge, link, “connection”
Relation among nodes
E.g., reports to

12. Trees, Hierarchies Representations
Pervasive
Family histories, ancestries
File/directory systems on computers
Organization charts
Animal kingdom: Phylum,…, genus,…
Object-oriented software classes …
Principle representations:
Node-link
Space-filling
Also, matrix (later)

13. Trees, Networks, and Graphs
Visualizing trees
Indented, node link, enclosure, layered
Visualizing graphs
Node link, matrix, network summarizations
Spatial layout
Primary concern of graph drawing is the spatial layout of nodes and edges
Often goal is to effectively depict the graph structure
Connectivity, path-following
Network distance
Clustering
Ordering (e.g., hierarchy level)

14. Trees Trees, or Hierarchies, or rooted-trees
Recursion makes it elegant and fast to draw trees
Visual representations
Indentation
Node link
Enclosure
Layering …
Complete listing of visual forms follows

15. Layouts E.g., Rectilinear, BubbleTree, Treemap
Layouts for 3228 nodes

16. Visual Encodings of Trees Munzner Taxonomy
Node link - A
Depth, vertical position
Layered node-link
Depth, horizontal pos.
“Icicle”
Radial node-link - D
Depth, dist. (from center)
Concentric circles
Depth, distance
Nested circles with radial containment
Treemap - E
containment, nesting level show tree depth
Indented

17. Trees Indentation Simple, often used, pros and cons
Place all items along vertically spaced rows
Indentation used to show parent/child relationships
Commonly used as a component in an interface
Breadth and depth contend for space
Often requires a great deal of scrolling

18. Degree Of Interest (DOI)Trees cf. Heer et al.
Indented tree
Also, size of word increases as user browses
“Focus + Context” technique
“See all with items of interest more detail”
Navigation (interaction) changes view
Often used strategy
Cf. reference model (next slide)

19. Trees Indentation
“Word tree” – IBM Many Eyes site

20. Visualization Pipeline: Some Detail
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
View change through interaction
Paradigm example of “focus + context”
Viewing all with details of some
User control of focus

21. (Simple) Node-Link Diagrams
Root at top, leaves at bottom is very common
Root can be at center, as well, with leaves growing out
Radial layout

22. Trees for Decisions, too NY Times, 2012
Engaging use of interactivity
Binary tree for electoral outcomes
Just “battleground” states
Or REALLY big

23. Tree “Layout Algorithm” For node-link diagrams
“Graph drawing” algorithms studied in their own right
Subfield of computer science
… and other disciplines
A basic node-link tree drawing
algorithm:
Recursive algorithm
Height on separate levels to indicate
level
Width in unique columns
Make room for subtrees upwards
Potential problems
For top-down, width of fan-out uses up horizontal real estate very quickly
At level n, there are (can be) 2n nodes
Tree might grow a lot along one particular branch
Hard to draw it well in view without knowing how it will branch

24. Better
Regions compressed horizontally

25. Reingold-Tilford Algorithm
Compact layout
Uses symmetry
Depth on levels
Applet

26. SpaceTree Conventional 2D layout techniques + view techniques
Video & Demo (planaria.avi)
Vertical or horizontal
Subtrees are triangles
Size indicates depth
Shading indicates number of nodes inside
Navigate by clicking on nodes
Strongly restrict zooming
Design Features
Make labels readable
Maximize number of levels opened
Decompose tree animation
Use landmarks
Use overview and dynamic filtering

27. Containment for Hierarchy GrouseFlocks
Uses containment to show graph hierarchy structure
Archambault et al. ’08 from Munzner
Several alternative hierarchies built from the same graph.
Hierarchy alone is shown in the top row
Bottom row combines the graph encoded with connection with a visual representation of the hierarchy using containment

28. Space-Optimized Tree
Put root node at center, then draw children out radially
Key: Smart positioning to optimize placement of braches (Voronoi diagram-like approach)

29. Trees Radial node-link diagrams
Simple radial layout
Just lay nodes equidistant
Lay out nodes in concentric circles
Vertices with no pred-ecessors placed in center
Descendants are placed on the next circle and so on
Works fine with some examples
But, in general leaves much white space

30. Trees Radial node-link diagrams
One approach is to have node-link diagram in polar coordinates
Radius encodes depth with root in center
Angular sectors assigned to subtrees
Or, just lay equidistant

31. Trees Balloon tree node-link diagrams
Compact drawing area by placing vertices in “balloons” around tree root
Can control:
angle for children of each vertex
preferred spacing between parent and child vertex
angle for children of root vertex
start angle for children of root vertex
minimal spacing between two vertices.

32. Node-Link Problems Scale Solutions
Tree breadth often grows exponentially
Quickly run out of space
Solutions
Hyperbolic layout
Filtering
Scrolling or panning
Zooming

33. Trees, Layered Diagrams
Similar to node-link layouts without edges
structured encoded using:
Layering
Adjacency
Alignment
Recursive subdivision of space
Apply same set of approaches as in node-link layout

34. Trees, Layered Diagrams Radial Layout
Similar to node-link layouts without edges
structured encoded using:
Layering
Adjacency
Alignment
Recursive subdivision of space
Apply same set of approaches as in node-link layout

35. Degree-of-Interest Trees Focus + Context display
Trees quickly degrade into line
Use focus + context technique to control how a tree is drawn
Combine multiple approaches:
Expanded DOI computation
Logical filtering to elide nodes
Geometric scaling
Semantic scaling
Clustered representation of large unexpended branches
Animated transition

36. Example Operations
Example Operations

37. Compression For nodes: compress to fit (compress in X or in Y)
Within-node
compression
Data deletion
Word abbreviation
Node rotation

38. FlexTree
Horizontally-drawn tree with compression along vertical dimension
One focus is on showing decision trees well
Contextual multi-foci view
Basic idea: Push all nodes down as far as you can
Song, Curran & Sterritt Information Visualization ‘04

39. FlexTree Bar Chart and Partial Viewsxx

40. FlexTree Full Tree View
xxx

41. FlexTree Node Tree
xxx

42. FlexTree As Decision Tree
xxx

43. Tree Layout: Alternative Solutions
One approach - 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

44. Tree Hyperbolic layout of nodes
Tree layout – hyperbolic, decreasing area f(d) center
Layout and navigation
Interactive systems, e.g., web site

45. 2D Hyperbolic Browser Approach Comparison
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
Lamping and Rao, JVLC ‘96

46. 2D Hyperbolic Browser
Clicking on the blue node brings it into focus at the center

47. 2D Hyperbolic Browser Video
Clicking on the blue node brings it into focus at the center
Video
Hyperbolic_Browser_chi96_02_m1_35mb (local file)
CHI ‘95, Rao:
Demo from prefuse

48. 2D Hyperbolic Browser Key Attributes Problems
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)
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

49. 3-d hyperbolic tree using Prefuse

50. 3D Hyperbolic Browser Munzner, ~1995
Layout
Find a spanning tree from an input graph - Use domain-specific knowledge
Nodes are laid out on the surface of a hemisphere (vs. circle)
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
Drawing
Maintain target frame by showing less context surrounding node of interest during interactive browsing
Fill in more of the surrounding scene when the user is idle

51. 3d Hyperbolic Browser
Navigation

52. 3D Hyperbolic Browser Same transformations in 3D space
Munzner videos, H3

53. Visualization Pipeline: (again) Some Detail
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Shneiderman’s “Data Type x Task” taxonomy only in terms of data to be displayed (Dataset)
E.g., 1D, 2D, 3D, n-dimensions
Card et al. model splits out “Visual Form”, after “Visual Mapping”
So, e.g., 3D (or n-D) data can be displayed in 2D space (dimensionality reduction)

54. Visualization Pipeline: Some Detail
Raw
Information
Visual
Form
Dataset
Views
User
- Task
Data
Transformations
Mappings
View F
F -1
Interaction
Perception
Also, Hyperbolic Browser illustrates change through interaction
Paradigm example of “focus + context”
Viewing all with details of some
User control of focus

55. Another 3D Approach Cone Trees
Add a third dimension into which layout can go
Top-down and centered techniques
Children of a node are laid out in a cylinder “below” the parent
Siblings live in one of the 2D planes
Cone trees
Xerox PARC
3D views of hierachies, e.g., file systems
Video
0:52-0:58, 1:21-1:28

56. Cone Trees Pros Cons More effective area to lay out tree
Use of smooth animation to help person track updates
Aesthetically pleasing
Cons
As in all 3D, occlusion obscures some nodes
Non-trivial to implement and requires some graphics horsepower

57. Tree/Hierarchical Data
An early, well known example
The Information Visualizer: An Information Workspace by G. R. Robertson, S. K. Card, J. M. Mackinlay, 1991 CACM

58. Problems with 3D
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)
SpaceTree presented earlier

59. Trees: Enclosure Diagrams

60. Trees: Enclosure Diagrams
Encode structure using spatial enclosure
Often referred to as “treemaps”
Shneiderman and group
Benefits
Provides single view of entire tree
Easier to spot small / large nodes
Problems
Difficult to accurately read depth

61. Treemaps Layout
Recursively fill space based on a size metric for nodes
E.g., n files
Enclosure indicates hierarchy
Additional measures can control aspect ratio of cells
Most often use rectangles, but other shapes possible
Square, circle, voronoi tessellation
Another example G H C D B A E F

62. Treemaps Wall Street Journal, MarketWatch, Map of the Market
Friday, 1/31/14, 1:45 CST
This treemap works, others not so much
Here, stock sectors (labeled) are first level
Individual stocks (within sectors) are next level
Node size is size of company

63. Treemaps Wall Street Journal, MarketWatch, Map of the Market
Friday, 1/31/14, 1:45 CST
This treemap works pretty well with no “training”
Training is good for others…

65. Treemap Layout in rectangular and non-rectangular space

66. Treemap Again, layout in non-rectangular space

67. Trees, more

68. Trees, yet more

69. Web Pages & Videos Trees
DOI trees
NY Times “election decision tree”:
Reingold-Tilford algorithm applet:
SpaceTree: , have planaria.avi
Hyperbolic tree browser – CHI ‘95, Rao:
Local copy: Hyperbolic_Browser_chi96_02_m1_35mb
Munzner videos, H3:
Cone Trees videos:
0:52-0:58, 1:21-1:28
Map of the market:
Tree poster:
vtk graph and viewing:
Also, “popular vtk videos”: Xx

70. End .