Cours de Visualisation d'InformationInfoVis Lecture

Hierarchies and Trees 1

Frédéric VernierEnseignant-Chercheur LIMSI-CNRS

Maître de conf Paris XI

Inspired from CS 7450 - Information Visualization

Jan. 10, 2002

John Stasko

2From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Hierarchies

DefinitionData repository in which cases are related

to subcasesCan be thought of as imposing an

ordering in which cases are parents or ancestors of other cases

3From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Hierarchies in the World

PervasiveFamily histories, ancestriesFile/directory systems on computersOrganization chartsAnimal kingdom: Phylum,…, genus,…Object-oriented software classesSpecies history

Y axis = timeIs it really discrete ?

4From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Trees

Hierarchies often represented as treesDirected, acyclic graph

Two main representation schemesNode-link (1/2)Space-filling (2/2)

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Node-Link Diagrams

Root at top, leaves at bottom is very common

Or left->right

Aligned / no brotherhood

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Sample Representation

Johnson & Shneiderman, ‘91

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Examples

Good for?

Bad for?

Search

Understanding structure

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Why Put Root at Top?

Root can be atcenter with levelsgrowing outwardtoo

Can any nodebe the root?

Pre-attentively ?

9From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Drawing a Tree

How does one draw this?• DFS• Percolate requirements upward

10From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Potential Problems

For top-down, width of fan-out uses up horizontal real estate very quicklyAt level n, there are 2n nodes for binary

treeTree might grow a lot along one

particular branchHard to draw it well in view without

knowing how it will branch

11From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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

12From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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 parentSiblings live in one of the 2D planes

13From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Cone Trees

Developed atXerox PARC

3D views ofhierarchiessuch as filesystems

Robertson, Mackinlay, Card ‘91

14From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Alternate Views

15From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Cone Trees

PositiveMore effective area

to lay out treeUse of smooth

animation to help person track updates

Aesthetically pleasing

NegativeAs in all 3D, occlusion

obscures some nodesNon-trivial to

implement and requires some graphics horsepower

Read in perspectiveDifficult if too muchAnti-aliasing = more

horsepowerBigger font = lost of

screen real estate

16From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Alternative Solutions

Change the geometryApply a hyperbolic transformation to

the spaceRoot is at center, subordinates aroundApply idea recursively, distance

decreases between parent and child as you move farther from center, children go in wedge rather than circle

17From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Hyperbolic Browser

Focus + Context TechniqueDetailed view blended with a global

viewFirst lay out the hierarchy on the

hyperbolic planeThen map this plane to a diskStart with the tree’s root at the

center Use animation to navigate along this

representation of the plane

Lamping and Rao, ‘94

18From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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

54

3

Clicking on the bluenode brings it into focus at the center

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Watch it Work

Demo from Inxight web site

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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 focusDon’t draw objects when far enough

from root (simplify rendering)

22From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Problems

OrientationWatching the view can be disorientingWhen 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 canHave fun with the math!

24From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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H3Viewer

Munzner, ‘98

Video

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Layout

Find a spanning tree from an input graphUse domain-specific knowledge

Layout algorithmNodes are laid out on the surface of a

hemisphereA bottom-up pass to estimate the radius

needed for each hemisphereA top-down pass to place each child

node on its parental hemisphere’s surface

26From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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/

29From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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, ‘94

30From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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

Diamonds are (mostly) not permittedThe ancestors of any node form a tree

of contexts

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Example

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Composition

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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.

34From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Multitrees contain Topological Trees

Topological tree or t-tree: an undirected graph, that is a connected graph without cycles

M-trees are not t-trees; they have undirected cycles

However, m-trees contain large t-trees.

The ancestors and descendants of a unique path is a t-tree

35From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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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Diamonds Are Forever

Sometimes, diamonds will not go away

People want to put the same item in more than one place in the tree.A set of documents organized both

alphabetically and by dateTelephone directory designed for lookup

by name or by phone numberOrganize sub-m-trees beneath more

general structures at the diamond level

41From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Organization of Roots

No top-down structure over the set of all roots

To guarantee a view of all roots, introduce an “artificial” leaf (descendant of all roots), whose upward view (by design) is a tree of all roots

42From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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Multitree Issues

Reuse out of contextWhen constructing a m-tree, fragments

may not hang togetherAdd or include new fragments to relate

pieces in the new m-treeConstruction

By hand is the most common way.Perhaps automatic, along hypertext

links, so long as no 2 hyperlink paths lead back to the same page!

43From J. Stasko lecture - CS 7450 – Spring 2002 – Georgia

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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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References

Spence and CMS texts

All referred to papers

Cai & Krohne and Pan & Wang F ‘99

slides

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Upcoming

Space-filling tree representationsGraphs and networks