multivariate data & representations

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Multivariate Data &Representations

CS 7450 - Information VisualizationJan. 15, 2004John Stasko

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Agenda

• Data forms and representations• Basic representation techniques• Multivariate (>3) techniques

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Data Sets

• Data comes in many different forms• Typically, not in the way you want it

• How is stored (in the raw)?

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Example

• Cars− make− model− year− miles per gallon− cost− number of cylinders− weights− ...

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Example

• Web pages

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Data Tables

• Often, we take raw data and transform it into a form that is more workable

• Main idea:− Individual items are called cases− Cases have variables (attributes)

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Data Table Format

Case1 Case2 Case3 ...

Variable1

Variable2

Variable3

...

Value11 Value21 Value31



Think of as a functionf(case1) = <Val11, Val12,…>

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Example

People in class

Mary Jim Sally Mitch ...

SSN

Age

Hair

GPA

...

145 294 563 823

23 17 47 29

brown black blonde red

2.9 3.7 3.4 2.1

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Example

Baseballstatistics

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Variable Types

• Three main types of variables− N-Nominal (equal or not equal to other

values)Example: gender

− O-Ordinal (obeys < relation, ordered set)Example: fr,so,jr,sr

− Q-Quantitative (can do math on them)Example: age

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Metadata

• Descriptive information about the data− Might be something as simple as the type of

a variable, or could be more complex− For times when the table itself just isn’t

enough− Example: if variable1 is “l”, then variable3

can only be 3, 7 or 16

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How Many Variables?

• Data sets of dimensions 1, 2, 3 are common

• Number of variables per class− 1 - Univariate data− 2 - Bivariate data− 3 - Trivariate data− >3 - Hypervariate data

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Representation

• What’s a common way of visually representing multivariate data sets?

• Graphs!

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Good Example

www.nationmaster.com

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Basic Symbolic Displays

• Graphs • Charts• Maps• Diagrams

From:S. Kosslyn, “Understanding chartsand graphs”, Applied CognitivePsychology, 1989.

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1. Graph

Showing the relationships between variables’values in a data table

0

20

40

60

80

100

1stQtr

2ndQtr

3rdQtr

4thQtr

EastWestNorth

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Properties

• Graph− Visual display that illustrates one or more

relationships among entities− Shorthand way to present information− Allows a trend, pattern or comparison to be

easily comprehended

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Issues

• Critical to remain task-centric− Why do you need a graph?− What questions are being answered?− What data is needed to answer those

questions?− Who is the audience?

time

money

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Graph Components

• Framework− Measurement types, scale

• Content− Marks, lines, points

• Labels− Title, axes, ticks

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Other Symbolic Displays

• Chart• Map• Diagram

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2. Chart

• Structure is important, relates entities to each other• Primarily uses lines, enclosure, position to link entities

Examples: flowchart, family tree, org chart, ...

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3. Map

• Representation of spatial relations• Locations identified by labels

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Choropleth Map

Areas are filledand coloreddifferently toindicate someattribute of thatregion

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Cartography

• Cartographers and map-makers have a wealth of knowledge about the design and creation of visual information artifacts− Labeling, color, layout, …

• Information visualization researchers should learn from this older, existing area

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4. Diagram

• Schematic picture of object or entity• Parts are symbolic

Examples: figures, steps in a manual, illustrations,...

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Details

• What are the constituent pieces of these four symbolic displays?

• What are the building blocks?

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Visual Structures

• Composed of− Spatial substrate− Marks− Graphical properties of marks

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Space

• Visually dominant• Often put axes on space to assist• Use techniques of

composition, alignment, folding,recursion, overloading to 1) increase use of space2) do data encodings

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Marks

• Things that occur in space− Points− Lines− Areas− Volumes

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Graphical Properties

• Size, shape, color, orientation...

Spatial properties Object properties

Expressingextent

Differentiatingmarks

PositionSize Grayscale

Orientation ColorShapeTexture

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Back to Data

• What were the different types of data sets?

• Number of variables per class− 1 - Univariate data− 2 - Bivariate data− 3 - Trivariate data− >3 - Hypervariate data

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Univariate Data

• Representations

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5

3

1

Bill

0 20

Mean

low highMiddle 50%

Tukey box plot

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What goes where

• In univariate representations, we often think of the data case as being shown along one dimension, and the value in another

Linegraph

Bargraph

Y-axis is quantitativevariable

See changes overconsecutive values

Y-axis is quantitativevariable

Compare relative pointvalues

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Alternative View

• We may think of graph as representing independent (data case) and dependent (value) variables

• Guideline:− Independent vs. dependent variables

Put independent on x-axisSee resultant dependent variables along y-axis

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Bivariate Data

• Representations

Scatter plot is common

price

mileage

Two variables, want tosee relationship

Is there a linear, curved orrandom pattern?

Each mark is nowa data case

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Trivariate Data

• Representations

3D scatter plot is possible

horsepower

mileage

price

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Alternative Representation

Still use 2D but havemark propertyrepresent thirdvariable

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Alternative Representation

Represent each variablein its own explicit way

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Hypervariate Data

• Ahhh, the tough one• Number of well-known visualization

techniques exist for data sets of 1-3 dimensions− line graphs, bar graphs, scatter plots OK− We see a 3-D world (4-D with time)

• What about data sets with more than 3 variables?− Often the interesting, challenging ones

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Multiple Views

Give each variable its own display

A B C D E1 4 1 8 3 52 6 3 4 2 13 5 7 2 4 34 2 6 3 1 5

A B C D E

1

2

3

4

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Scatterplot Matrix

Represent each possiblepair of variables in theirown 2-D scatterplot

Useful for what?Misses what?

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Chernoff Faces

Encode different variables’ values in characteristicsof human face

http://www.cs.uchicago.edu/~wiseman/chernoff/http://hesketh.com/schampeo/projects/Faces/chernoff.html

Cute applets:

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Star Plots

Var 1

Var 2

Var 3Var 4

Var 5

Value

Space out the nvariables at equalangles around a circle

Each “spoke” encodesa variable’s value

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Star Plot examples

http://seamonkey.ed.asu.edu/~behrens/asu/reports/compre/comp1.html

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Star Coordinates

E. Kandogan, “Star Coordinates: A Multi-dimensional VisualizationTechnique with Uniform Treatment of Dimensions”, InfoVis 2000Late-Breaking Hot Topics, Oct. 2000 Demo

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Parallel Coordinates

• What are they?− Explain…

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V1 V2 V3 V4 V5

Encode variables alonga horizontal row

Vertical line specifiesvalues

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Parallel Coords Example

Basic

Grayscale

Color

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Application

• System that uses parallel coordinates for information analysis and discovery

• Interactive tool− Can focus on certain data items− Color

Taken from:

A. Inselberg, “Multidimensional Detective”InfoVis ‘97, 1997.

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Discuss

• What was their domain?• What was their problem?• What were their data sets?

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The Problem

• VLSI chip manufacture• Want high quality chips (high speed) and

a high yield batch (% of useful chips)• Able to track defects• Hypothesis: No defects gives desired chip

types• 473 batches of data

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The Data

• 16 variables− X1 - yield− X2 - quality− X3-X12 - # defects (inverted)− X13-X16 - physical parameters

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Parallel Coordinate Display

Yikes!But notthat bad

yield &quality defects parameters

Distributionsx1 - normalx2 - bipolar

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Top Yield & Quality

defects

Have some defects

split

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Minimal Defects

Not thehighestyields andquality

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Best Yields

Appears thatsome defectsare necessaryto produce the best chips

Non-intuitive!

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Xmdv

Toolsuite createdby Matthew Wardof WPI

Includes parallelcoordinate views

Demo

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Parallel Coordinate Tree

D. Brodbeck and L. Girardin, "Visualization of Large-Scale Customer Satisfaction Surveys Using a Parallel Coordinate Tree", InfoVis ’03.

Demo

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• Technique− Strengths?− Weaknesses?

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Sliding Rods

T. Lanning, K. Wittenburg, et al, "Multidimensional Information Visualization through Sliding Rods", Proceedings of AVI 2000

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Administratia

• Computer accounts• HW 2 due Tuesday

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Upcoming

• Multivariate vis tools− Reading:

Eick paper

• Visual perception• Tufte (please be reading)

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Sources Used

CMS bookReferenced articlesMarti Hearst SIMS 247 lecturesKosslyn ‘89 articleA. Marcus, Graphic Design for Electronic Documents

and User InterfacesM. Monmonier, How to Lie with MapsW. Cleveland, The Elements of Graphing DataC. H. Yu, Visualization Techniques of Different Dimensionshttp://seamonkey.ed.asu.edu/~behrens/asu/reports/compre/comp1.htmlhttp://www.csc.ncsu.edu/faculty/healey/PP/PP.html