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

Visualization Taxonomies and Techniques

Trees and Graphs

University of Texas – Pan American

CSCI 6361, Spring 2014

Tonight:

• More about Taxonomies and Techniques– 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

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)

Visualization Pipeline:Mapping Data to Visual Form (Card et al., North)

• 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

RawInformation

VisualFormDataset Views

User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

Visualization Pipeline:Mapping Data to Visual Form (Card et al., North)

• 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

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

Visualization Pipeline: Visualization Stages

• 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

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

Visualization Pipeline:Information Structure

• 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

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

Visualization Pipeline:Tonight

• 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

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

Visualization Pipeline:Some Detail

• 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)

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

Trees, Networks and Graphs

• 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

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

• Tree is a graph = set of V, E– Root (top), leaves (bottom),

parents, children

Trees, HierarchiesAbout

• 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

Trees, HierarchiesRepresentations

• 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)

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)

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

LayoutsE.g., Rectilinear, BubbleTree, Treemap

• Layouts for 3228 nodes

Visual Encodings of TreesMunzner 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

TreesIndentation

• 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

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)

http://vis.stanford.edu/papers/doitrees-revisited

TreesIndentation

• “Word tree” – IBM Many Eyes site


• View change through interaction

• Paradigm example of “focus + context”

– Viewing all with details of some– User control of focus

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

(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

Trees for Decisions, tooNY Times, 2012

• Engaging use of interactivity

• Binary tree for electoral outcomes

• Just “battleground” states

– Or REALLY big

• http://elections.nytimes.com/2012/results/president/scenarios

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

Better

• Regions compressed horizontally

Reingold-Tilford Algorithm

• Compact layout • Uses symmetry • Depth on levels

• Applet• http://www.cfm.brown.edu/people/hu/

cs252/online.html

SpaceTree

• Conventional 2D layout techniques + view techniques

– Video & Demo (planaria.avi)

• http://www.cs.umd.edu/hcil/spacetree/

• 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

Containment for HierarchyGrouseFlocks

• 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

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)

TreesRadial 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

http://www.nevron.com/Gallery.DiagramFor.NET.AutomaticLayouts.RadialGraphLayout.aspx

TreesRadial 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

http://seeingcomplexity.w3o5rdpress.com/2011/02/05/hierarchical-edge-bundles/

TreesBalloon 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.

http://www.nevron.com/Gallery.DiagramFor.NET.AutomaticLayouts.BalloonTreeLayout.aspx

Node-Link Problems

• Scale– Tree breadth often grows exponentially– Quickly run out of space

• Solutions– Hyperbolic layout– Filtering– Scrolling or panning– Zooming

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

http://ivtk.sourceforge.net/

Trees, Layered DiagramsRadial 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

http://hci.stanford.edu/jheer/files/zoo/

Degree-of-Interest TreesFocus + 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

Example Operations

• Example Operations

Compression

• For nodes: compress to fit (compress in X or in Y)

• Within-node

compression – Data deletion – Word abbreviation – Node rotation

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

FlexTreeBar Chart and Partial Views

• xx

FlexTreeFull Tree View

• xxx

FlexTreeNode Tree

• xxx

FlexTree As Decision Tree

• xxx

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

TreeHyperbolic layout of nodes

• Tree layout – hyperbolic, decreasing area f(d) center• Layout and navigation

• Interactive systems, e.g., web site

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

– Lamping and Rao, JVLC ‘96


• Clicking on the blue node brings it into focus at the center

2D Hyperbolic BrowserVideo

• Clicking on the blue node brings it into focus at the center

• Video – Hyperbolic_Browser_chi96_02_m1_35mb (local file)– CHI ‘95, Rao: http://www.youtube.com/watch?v=pwpze3RF55o

• Demo from prefuse


• 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)

• 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

3-d hyperbolic tree using Prefuse

3D Hyperbolic BrowserMunzner, ~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

3d Hyperbolic Browser

• Navigation


• Same transformations in 3D space

• Munzner videos, H3 – http://graphics.stanford.edu/videos/h3/

Visualization Pipeline:(again) Some Detail

• 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)

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception


• Also, Hyperbolic Browser illustrates change through interaction

• Paradigm example of “focus + context”– Viewing all with details of some– User control of focus

RawInformation


User - Task

DataTransformations

VisualMappings

ViewTransformations

F F -1

Interaction

VisualPerception

Another 3D ApproachCone 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

• http://www.youtube.com/watch?v=vbzozDCW_Bg• 0:52-0:58, 1:21-1:28

Cone Trees

• Pros – 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

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

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

Trees: Enclosure Diagrams

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

TreemapsLayout

• 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

TreemapsWall 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

http://www.marketwatch.com/tools/stockresearch/marketmap

TreemapsWall Street Journal, MarketWatch, Map of the Market

• Friday, 1/31/14, 1:45 CST

• http://www.marketwatch.com/tools/stockresearch/marketmap

• This treemap works pretty well with no “training”

• Training is good for others…

http://www.marketwatch.com/tools/stockresearch/marketmap

Treemap

• Layout in rectangular and non-rectangular space– http://hci.stanford.edu/jheer/files/zoo/

Treemap

• Again, layout in non-rectangular space

http://www.flickr.com/photos/a4r1enamontanus/2037614308/sizes/o/in/photostream/

Trees, more

http://www.randelshofer.ch/treeviz/index.html

Trees, yet more

http://vcg.informatik.uni-rostock.de/~hs162/treeposter/poster.html

Web Pages & VideosTrees

• DOI trees• NY Times “election decision tree”: http://elections.nytimes.com/2012/results/president/scenarios

• Reingold-Tilford algorithm applet: http://www.cfm.brown.edu/people/hu/cs252/online.html

• SpaceTree: http://www.cs.umd.edu/hcil/spacetree/ , have planaria.avi

• Hyperbolic tree browser – CHI ‘95, Rao: http://www.youtube.com/watch?v=pwpze3RF55o

– Local copy: Hyperbolic_Browser_chi96_02_m1_35mb

• Munzner videos, H3: http://graphics.stanford.edu/videos/h3/

• Cone Trees videos:• http://www.youtube.com/watch?v=vbzozDCW_Bg

• 0:52-0:58, 1:21-1:28

• Map of the market: http://www.marketwatch.com/tools/stockresearch/marketmap

• Tree poster: http://vcg.informatik.uni-rostock.de/~hs162/treeposter/poster.html

• vtk graph and viewing: http://www.youtube.com/watch?v=Yr1eGXTNryE&list=PLDmjJ1FAXPR2FBwhEiGy3rLm7jCPBvWyr&index=34

– Also, “popular vtk videos”: http://www.youtube.com/playlist?list=PLDmjJ1FAXPR2FBwhEiGy3rLm7jCPBvWyr

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Documents

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