© Silvia Miksch

Part 1

Geometric TechniquesScatterplots,Parallel Coordinates, ...

© Silvia Miksch

Geometric Techniques• Basic Idea

– Visualization of Geometric Transformationsand Projections of the Data

• Scatterplots [Cleveland 1993]• Parallel Coordinates [Inselberg 1985/1990]• Prosection Views [Spence 95]• Landscape [Wise, et al. 1995]• ThemeRiver [Havre, et al 2000]• Hyperslice [van Wijk, et al 1993]

[Keim, 2001]

© Silvia Miksch

Basic Idea: Scatterplots• Visualizes a Relation (Correlation)

between two Variables X and Y– e.g., weight and height

• Individual Data Points are Represented– in 2D

• where axes represent the variables• X on the horizontal axis• Y on the vertical axis

– in 3D– in ...

© Silvia Miksch

Example: Scatter PlotHouse data:

Price and Number of bedrooms

50K 100K 150K 200K 250K 300K

1

2

3

4

5

6

Number of Bedrooms

Price (£)

User can identify globaltrends, local trade-offsand outliners.

© Silvia Miksch

Examples: Scatterplots (1/3)No relationship Strong linear (positive correlation)

Strong linear (negative correlation) Exact linear (positive correlation)

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Examples: Scatterplots (2/3)Quadratic relationship Exponential relationship

Sinusoidal relationship (damped) Outlier

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Examples: Scatterplots (3/3)Variation of Y doesn't depend on X (homoscedastic)

Variation of Y does depend on X (heteroscedastic)

© Silvia Miksch

Scatterplot - Conditioning PlotOne limitation of thescatterplot matrix isthat it cannot showinteraction effects withanother variable

Purpose:Check pairwiserelationship betweentwo variablesconditional on a thirdvariable

temp: torque versus time

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3 D Data in the Box3 D Data Set of50 Observations

in the Box

Scatterplot Matrixof all pairwiseScatterplots

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Example: Cars[Becker & Cleveland, 1996]

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Example: Cars - Scatterplots

m x m scatterplots

diagonal = same(m2 - m)

left -right the same(m2 - m)/2

© Silvia Miksch

Example 2 - Cars - Scatterplot

© Silvia Miksch

3 D Scatterplot plus Color

© Silvia Miksch

Scatterplot & SDOF (1/2)

© Silvia Miksch

Scatterplot & SDOF (2/2)

© Silvia Miksch

Basic Idea: Parallel Coordinates• Assigns one Vertical Axis to each Variable

– Evenly spaces these axes horizontally– Traditional Cartesian Coordinates

• All axes are mutually perpendicular

• Layout: k Parallel Axes• Axes to [min, max]

– Scaling individually for each variable• Polygonal Line

– Every data item correspond to a polygonal line– Intersects each of the axes at the point– Corresponds to the value for the attribute

[Inselberg and Dimsdale, 1990]

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Parallel Coordinates[Inselberg and Dimsdale, 1990]

© Silvia Miksch

Parallel Coordinates

© Silvia Miksch

Parallel Coordinates– Basic• 6-dim. Point with

cordinates (-5,3,4,-2,0,1)T

• one line:point in PC

• one circle:

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Visualization of Correlation• Discover the

Correlation

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Problems with Parallel Cord.• Polygons need to Much Space

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Color in Parallel Coordinates

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Hierach Parallele Coord.

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Example: Cars - Parallel Cord.

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Parallel Coordinates• Demo Programs:

Parallel Coordinates VisualizationApplet

http://csgrad.cs.vt.edu/~agoel/parallel_coordinates/

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Benefits and Limitations• Benefit

– Represent data greater than three dimensions– Opportunities for human pattern recognition– Flexibility: each coordinate can be individually

scaled– Zooming in or out: effectively brushing out or

eliminating portions of the data set• Limitations

– As the number of dimensions increases, theaxes come closer to each other, making it moredifficult to perceive patterns

© Silvia Miksch

Prosection Views• Similar to Scatterplots• m-dim Data Sets• Operators

– Projections– Selections

• Color Coding– customer’s requirements (different limits)

• yes: red or green• no: black, dark gray, light gray, and white

[Spence, et al. 1995]

© Silvia Miksch

The Prosection MatrixDesign of a chair seat

Area

Thickness

Thickness

Area

too heavy

too uncomfortable

too flexible

too large

A design is represented bya point in Area-Thicknessspace

Various performance limitsrestrict the range ofpossible designs

[ © 2001 Robert Spence]

© Silvia Miksch

The Prosection MatrixProblem: we don’t know wherethe green area is located

Area

Thickness

Moreover, there are typicallymany parameters (not 2) andmany performance limits(not 2)

Solution?Either iterative search (human, automated or mixed) orgeneration of data to visualise.

[ © 2001 Robert Spence]

© Silvia Miksch

The Prosection Matrix [ © 2001 Robert Spence]

© Silvia Miksch

Color Coding

Par 2

Par 1

Upper Limit S1

Lower Limit S1

Upper Limit S2

Lower Limit S2

Tolerance Region

Satisfied all limits

Satisfied all theperformance limits,but outsideone parameter limit= not manufactured

Fail one or moreperformance limits,but manufactured

Fail oneperformance limits,but manufactured

Fail one or moreperformance limits,not manufactured

Parameter limits vs Performance limits

© Silvia Miksch

The Prosection Matrix• A Prosection:

Projection of a section

[ © 2001 Robert Spence]

© Silvia Miksch

The Prosection Matrix

Prosection Matrixfor the lamp design

A difficult cognitiveproblem is eased bya simple perceptualtask

[ © 2001 Robert Spence]

Tolerances onparameter values

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The Prosection Matrix [ © 2001 Robert Spence]

RawData

ModelParameters Performances

Selection Encoding Presentation

User

Interaction

Customer’sPerformanceRequirements

Visualization tool designer

The visualization tool (e.g., Influence Explorer) designer must take intoaccount the need of the user to specify the model, the exploratory rangeof parameter values and the customer’s performance specifications, aswell as the selection, encoding and presentation of data.

© Silvia Miksch

LandscapeData needs to be transformed into a (possible artificial) 2Dspatial representation which preserves the characteristicsof the data

[Wise, et al. 1995]

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ThemeRiver:

Visualizing Theme Changes over Time

Susan Havre, Beth Hetzler, and Lucy NowellBattelle Pacific Northwest Division,Washington, USA

Applications I: Document Visualization

IEEE Symposium onInformation Visualization - InfoVis 2000

Excursus

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InfoVis 2000: Facts'n'Figures• October 9-10, 2000• Salt Lake City, Utah, USA• Annual Conference/Symposium

– 6th• Parent Conference

– IEEE Visualization 2000 ---- 11th• Proceedings:

– CD Rom– IEEE Computer Society, Los Alamitos, CA

© Silvia Miksch

IEEE Visualization 2000• Annual Conference• 11th

© Silvia Miksch

© Silvia Miksch

Types of Papers at InfoVis• Keynote Address

– Jock D. Mackinlay, University of Aarhus, DenmarkPresentation, Visualization, What's Next

• Coining the term InfoVis• Visual Data Mining• “Readings in InfoVis”

• 20 Papers - 5 Sessions• 6 Papers - Late Breaking Hot Topics• Capstone Address

– Nahum Gershon, MITREVisual Storytelling - Where Technology and CultureMeet © Silvia Miksch

Session Topics• Visual Querying and Data Exploration• Graphs and Hierarchies• Taxonomies, Frameworks, and

Methodology• Applications I:

– Document Visualization, CollaborativeVisualization, Techniques

• Applications II:– Algorithm Visualization, 3D Navigation

© Silvia Miksch

ThemeRiver:

Visualizing Theme Changes over Time

Susan Havre, Beth Hetzler, and Lucy NowellBattelle Pacific Northwest Division,Washington, USA

Applications I: Document Visualization

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Idea• A Large Collection of Documents• Themes Changes• River Metaphor

- “helps users to identify time-relatedpatterns, trends, and relationships across alarge collection of documents”

• A Prototype System

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ThemeRiverTM

Data set:collection of

speeches,interviews,

articles, andother text

associatedwith Fidel

Castro

© Silvia Miksch

Histograms

Data set:collection of

speeches,interviews,

articles, andother text

associatedwith Fidel

Castro

© Silvia Miksch

User Interactions• Display Topic and Event Labels• Display Time and Event Grid Lines• Display the Raw Data Points• Choose Among Drawing algorithms for

the Currents and River

• Pan and Zoom – Other Time Periods or Parts of the River– More Detail or Broader Context

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Usability Evaluation• 2 Users & Questions:

– Do users understand the metaphor?– Can they identify themes that are more often

discussed?– Does the visualization help them raise new

questions about the data?– Do they interpret details of the visualization in

ways we had not expected?– How does their interpretation of the

visualization differ from that of a histogramshowing the same data?

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Evaluation Results• ThemeRiver Easy to Understand• Useful + / -

+ River Metaphor+ Abstraction to the Whole Collection+ Identifying Macro Trends

- Identifying Minor Trends

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Improvements• Features of the Histogram

– Seeing Numeric Values (on demand)– Total Number of Documents

• Features to Access the Documents• User-Defined Ordering

– Reorder the Theme Currents– Ordering by Correlation

• Parallel Rivers

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Impr.: Features of the Histogram

Data set:1990

AssociatedPress (AP)

newswire datafrom theTREC5

distributiondisks, a set ofover 100,000

documents

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Impr.: Parallel Rivers

Data set:compare 1990

Associated Press(AP)

AP with datafrom Washington,

D.C. and New Yorkfrom the

same time period

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Color Family

Tracking relatedthemes is simplified byassigning them to the

same color family. Thisensures relatedthemes appear

together and areidentifiable as a group.

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Conclusion• River Metaphors• Perception Principles [Ware 2000]

• Improvements Needed– Event Time Line - Automatically– Selecting and Ordering of Theme Currents– More Information/Data on Demand

© Silvia Miksch

Hyperslices• (m2 - m)/2 2D slices• Operator

– Selection

[ van Wiik, et al 1993]