Transcript Graphical/Visual Properties

Multivariate Data &
Representations
CS 7450 - Information Visualization
Jan. 20, 2005
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)?
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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
Value11
Value21
Value31
Variable2
Value12
Value22
Value32
Variable3
Value13
Value23
Value33
...
...
Think of as a function
f(case1) = <Val11, Val12,…>
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Example
Mary
Jim
Sally
Mitch
SSN
145
294
563
823
Age
23
17
47
29
Hair
brown
black
GPA
2.9
3.7
blonde
red
3.4
2.1
...
...
People in class
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Example
Baseball
statistics
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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 charts
and graphs”, Applied Cognitive
Psychology, 1989.
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1. Graph
Showing the relationships between variables’
values in a data table
100
80
60
East
40
West
North
20
0
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1st
Qtr
2nd
Qtr
3rd
Qtr
4th
Qtr
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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?
money
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time
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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 filled
and colored
differently to
indicate some
attribute of that
region
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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 space
2) 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
Expressing
extent
Position
Size
Grayscale
Differentiating
marks
Orientation
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Color
Shape
Texture
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Intermission
• Getting slides
• Getting papers
• Photos
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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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Bill
Tukey box plot
5
low
3
1
high
Mean
0
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Middle 50%
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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
Line
graph
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Bar
graph
Y-axis is quantitative
variable
Y-axis is quantitative
variable
See changes over
consecutive values
Compare relative point
values
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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-axis
See resultant dependent variables along y-axis
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Bivariate Data
• Representations
Scatter plot is common
price
Two variables, want to
see relationship
Each mark is now
a data case
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Is there a linear, curved or
random pattern?
mileage
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Trivariate Data
• Representations
3D scatter plot is possible
price
horsepower
mileage
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Alternative Representation
Still use 2D but have
mark property
represent third
variable
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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
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Multiple Views
Give each variable its own display
1
1
2
3
4
A
4
6
5
2
B
1
3
7
6
C
8
4
2
3
D
3
2
4
1
E
5
1
3
5
2
3
4
A B C D E
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Scatterplot Matrix
Represent each possible
pair of variables in their
own 2-D scatterplot
Useful for what?
Misses what?
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Chernoff Faces
Encode different variables’ values in characteristics
of human face
Cute applets:
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http://www.cs.uchicago.edu/~wiseman/chernoff/
http://hesketh.com/schampeo/projects/Faces/chernoff.html
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Star Plots
Var 1
Var 5
Var 2
Value
Var 4
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Var 3
Space out the n
variables at equal
angles around a
circle
Each “spoke” encodes
a 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 Visualization
Technique with Uniform Treatment of Dimensions”, InfoVis 2000
Late-Breaking Hot Topics, Oct. 2000
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Demo
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Parallel Coordinates
• What are they?
 Explain…
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Parallel Coordinates
Encode variables along
a horizontal row
Vertical line specifies
values
V1
V2
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V3
V4
V5
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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
yield &
quality
defects
parameters
Yikes!
But not
that bad
Distributions
x1 - normal
x2 - bipolar
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Top Yield & Quality
split
defects
Have some defects
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Minimal Defects
Not the
highest
yields and
quality
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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
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Parallel Coordinate Tree
Demo
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D. Brodbeck and L. Girardin, "Visualization of LargeScale Customer Satisfaction Surveys Using a Parallel
Coordinate Tree", InfoVis ’03.
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Parallel Coordinates
• Technique
 Strengths?
 Weaknesses?
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Sliding Rods
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T. Lanning, K. Wittenburg, et al,
"Multidimensional Information
Visualization through Sliding Rods",
Proceedings of AVI 2000
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Administratia
• Computer accounts
• HW 1 in today
• HW 3 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 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
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