Multivariate Data Sets

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Multivariate Data Sets

• CS 7450 - Information Visualization
• Aug. 29, 2000

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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
Value12 Value22 Value32
Dimensions
Value13 Value23 Value33
Think of as a function f(case1) ltVal11, Val12,gt
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Example
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
People in class
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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 lt 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 isnt 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
• gt3 - Hypervariate data

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Univariate Data

• Representations

Bill
7 5 3 1
Tukey box plot
Middle 50
low
high
Mean
0
20
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Bivariate Data

• Representations

Scatter plot is common
price
mileage
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Trivariate Data

• Representations

3D scatter plot is possible
price
horsepower
mileage
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Hypervariate Data

• 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 ones

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Multiple Views
Give each variable its own display
1
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
2
3
4
A B C D E
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Chernoff Faces
Encode different variables values in
characteristics of human face
Cute applet
http//www.cs.uchicago.edu/wiseman/chernoff/
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Star Plots
Var 1
Space out the n variables at equal angles around
a circle Each spoke encodes a variables value
Var 2
Var 5
Value
Var 3
Var 4
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Star Plot examples
http//seamonkey.ed.asu.edu/behrens/asu/reports/c
ompre/comp1.html
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Parallel Coordinates
Encode variables along a horizontal row Vertical
line specifies values
V1 V2 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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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 thehighestyields andquality
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Best Yields
Appears that some defects are necessary to
produce the best chips Non-intuitive!
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Another Problem

• Data concerning economic output of a country
  (fishing, mining, etc.)
• Eight variables
• Fit a model to the data set
• Model describes possible economic outputs

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Parallel Coordinates
Model boundary
Pick a value
Model boundary
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Another Technique

• Database of data items, each of n dimensions
• Issue a query that specifies a target value of
  the dimensions
• Often get back no exact matches
• Want to find near matches

Taken from D. Keim, H-P Kriegel, VisDB Database
Exploration Using Multid Vis, IEEE CGA, 1994.
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Relevance Factor

• How close an item is to the query

• Data items have some value that can be
  numerically quantified
• Each dimension is some distance away
• from query item
• Sum these up for total distance
• Relevance is inverse of distance

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Example

• 5 dimensions, integers 0-gt255
• Query 6, 210, 73, 45, 92
• Data item 8, 200, 73, 50, 91
• Distance 2 10 0 5 1 18
• Relevance 1275 - 18 1267

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Issues

• What if dimensions are real numbers or text
  strings?
• What if theyre the same type, but of different
  orders of magnitude?
• Have to define some kind of distance, then a
  weight function to multiply by

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Technique

• Calculate relevance of all data points
• Sort items based on relevance
• Use spiral technique to order the values
• Color items based on relevance

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Relevance Colors
Low
High
Empirically established
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Spiral Method
Highest relevancevalue in center,decreasing
valuesgrow outward
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Display Methodology
Example five-dimensional data
Same itemappears insame placein each window
Totalrelevance
Dim 1
Dim 2
Spiral in eachwindow
Dim 3
Dim 4
Dim 5
Items ordered by total relevance
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Figure from Paper
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Example Display
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Alternative

• Grouping arrangement
• Doesnt use multiple windows
• Create all relevance dimensional depictions for
  an item and group them
• Spiral out the different data items depictions

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Grouping Arrangement
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Example Display
8 dimensions
1000 items
Grouping
Multi-window
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Sources Used
CMS book Referenced articles Marti Hearst SIMS
247 lectures C. H. Yu, Visualization Techniques
of Different Dimensions http//seamonkey.ed.asu
.edu/behrens/asu/reports/compre/comp1.html