Multivariate Data & Representations

Multivariate Data &

Representations

CS 7450 - Information Visualization Jan. 15, 2004

John Stasko

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)?

Example

• Cars

−make

−model

−year

−miles per gallon

−cost

−number of cylinders

−weights

−...

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Example

• Web pages

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 Value₁₂ Value₂₂ Value₃₂ Value₁₃ Value₂₃ Value₃₃

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

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

Baseball statistics

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

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!

Good Example

www.nationmaster.com

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Basic Symbolic Displays

• Graphs Å

• Charts

• Maps

• Diagrams

From:

S. Kosslyn, “Understanding charts and graphs”, Applied Cognitive Psychology, 1989.

1. Graph

Showing the relationships between variables’

values in a data table

0 20 40 60 80 100

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

East West North

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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

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?

money

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Graph Components

• Framework

−Measurement types, scale

• Content

−Marks, lines, points

• Labels

−Title, axes, ticks

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, ...

3. Map

• Representation of spatial relations

• Locations identified by labels

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Choropleth Map

Areas are filled and colored differently to indicate some attribute of that region

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,...

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

Space

• Visually dominant

• Often put axes on space to assist

• Use techniques of

composition, alignment, folding, recursion, overloading to

1) increase use of space 2) do data encodings

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Marks

• Things that occur in space

−Points

−Lines

−Areas

−Volumes

Graphical Properties

• Size, shape, color, orientation...

Spatial properties Object properties Expressing

extent

Differentiating marks

Position

Size Grayscale

Orientation Color

Shape Texture

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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

Univariate Data

• Representations

7 5 3 1

Bill

0 20

Mean

low Middle 50% high

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 Bar

graph

Y-axis is quantitative variable

See changes over consecutive values

Y-axis is quantitative variable

Compare relative point values

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-axis

See resultant dependent variables along y-axis

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Bivariate Data

• Representations

Scatter plot is common

price

mileage

Two variables, want to see relationship

Is there a linear, curved or random pattern?

Each mark is now a data case

Trivariate Data

• Representations

3D scatter plot is possible

horsepower

mileage

price

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Alternative Representation

Still use 2D but have mark property

represent third variable

Alternative Representation

Represent each variable in 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

Multiple Views

Give each variable its own display

A B C D E 1 4 1 8 3 5 2 6 3 4 2 1 3 5 7 2 4 3 4 2 6 3 1 5

1

2

3

4

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Scatterplot Matrix

Represent each possible pair of variables in their own 2-D scatterplot

Useful for what?

Misses what?

Chernoff Faces

Encode different variables’ values in characteristics of human face

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Star Plots

Var 1

Var 2

Var 3 Var 4

Var 5

Value

Space out the n variables at equal angles around a circle

Each “spoke” encodes a variable’s value

Star Plot examples

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Star Coordinates

E. Kandogan, “Star Coordinates: A Multi-dimensional Visualization Technique with Uniform Treatment of Dimensions”, InfoVis 2000

Late-Breaking Hot Topics, Oct. 2000 Demo

Parallel Coordinates

• What are they?

−Explain…

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Parallel Coordinates

V1 V2 V3 V4 V5

Encode variables along a horizontal row

Vertical line specifies values

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.

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

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 not that bad

yield &

quality defects parameters

Distributions x1 - normal x2 - bipolar

Top Yield & Quality

defects split

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Minimal Defects

Not the highest yields and quality

Best Yields

Appears that some defects are necessary to produce the best chips Non-intuitive!

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Xmdv

Toolsuite created by Matthew Ward of WPI

Includes parallel coordinate views

Demo

Parallel Coordinate Tree

Demo

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Parallel Coordinates

• Technique

−Strengths?

−Weaknesses?

Sliding Rods

T. Lanning, K. Wittenburg, et al,

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Administratia

• Computer accounts

• HW 2 due Tuesday

Upcoming

• Multivariate vis tools

−Reading:

Eick paper

• Visual perception

• Tufte (please be reading)

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Sources Used

CMS book

Referenced articles

Marti Hearst SIMS 247 lectures Kosslyn ‘89 article

A. Marcus, Graphic Design for Electronic Documents and User Interfaces

M. Monmonier, How to Lie with Maps

W. Cleveland, The Elements of Graphing Data

C. H. Yu, Visualization Techniques of Different Dimensions

http://seamonkey.ed.asu.edu/~behrens/asu/reports/compre/comp1.html http://www.csc.ncsu.edu/faculty/healey/PP/PP.html