Marti Hearst

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SIMS 247 Lecture 4Graphing Multivariate
Information

• January 29, 1998

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Follow-up previous lecture

• Docuverse
• length of arc is proportional to
• number of subdirectories
• radius for a given arc is long enough to contain
  marks for all the files in the directory
• Nightingales coxcomb
• keep arc length constant
• vary radius length (proportional to sqrt(freq))

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Today Multivariate Information

• We see a 3D world
• How do we handle more than 3 variables?
• multi-functioning elements
• Tufte examples
• cinematography example
• multiple views

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Example Data Sets

• How do we handle 9 variables?
• Our web access dataset
• Factors involved in alcoholism
• ALCOHOL
• USE
• AVAILABILITY
• CONCERN ABOUT USE
• COPING MECHANISMS
• PERSONALITY MEASURES
• EXTROVERSION
• DISINHIBITION
• OTHER
• GENDER
• GPA

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Graphing Multivariate Information

• How do we handle cases with more than three
  variables?
• Scatterplot matrices
• Parallel coordinates
• Multiple views
• Overlay space and time
• Interaction/animation across time

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Multiple Variables Scatterplot Matrices(from
Wegman et al.)
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Multiple Variables Scatterplot Matrices(from
Schall 95)
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Multiple Views Star Plot(Discussed in Feinberg
79. Works better with animation. Example taken
from Behrans Yu 95.)
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Multiple Dimensions Parallel Coordinates(earthqu
ake data, color indicates longitude, y axis
severity of earthquake, from Schall 95)
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Multiple Dimensions Multivariate Star Plot(from
Behran Yu 95)
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Chernoff Faces

• Assumption people have built-in face recognizers
• Map variables to features of a cartoon face
• Example eyes
• location, separation, angle, shape, width
• Example entire face
• area, shape, nose length, mouth location, smile
  curve
• Originally tongue-in-cheek, but taken seriously
• Sometimes seems to work for small numbers of
  points

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Chernoff Example (Marchette)

• Three groups of points
• each drawn from a different distribution with 5
  variables
• First show scatter-plot matrix
• Then graph with Chernoff faces
• vary faces overall
• vary eyes
• vary mouth and eyebrows
• Which seems to be most effective?

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Chernoff Experiment (Marchette)
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Chernoff Experiment (Marchette)
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Chernoff Experiment (Marchette)
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Chernoff Experiment (Marchette)
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Overlaying Space and Time(Minards graph of
Napoleans march through Russia)
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A Detective Story(Inselberg 97)

• Domain Manufacture of computer chips
• Objectives create batches with
• high yield (X1)
• high quality (X2)
• Hypothesized cause of problem
• 9 types of defects (X3-X12)
• Some physical properties (X13-X16)
• Approach
• examine data for 473 batches
• use interactive parallel coordinates

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Multidimensional Detective

• Long term objectives
• high quality, high yield
• Logical approach given the hypothesis
• try to eliminate defects
• First clue
• what patterns can be found among batches with
  high yield and quality?

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Detectives arent intimidated!
X1 seems to be normally distributed X2 bipolar
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High quality yields obtained despite defects
good batches
X15 breaks into two clusters (important physical p
roperty)
some low X3 defect batches dont appear here
at least one good batch with defects
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Low-defect batches are not highest quality!
few defects
low yield, low quality
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Original plot shows defect X6 behaves
differently exclude it from the 9-out-of-10
defects constraint the best batches return
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Isolate the best batches.Conclusion defects are
necessary!
The very best batch has X3 and X6 defects
Ensure this is not an outlier -- look at top few
batches. The same result is found.
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How to graph web page traversals?
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References for this Lecture

• Visualization Techniques of Different Dimensions,
  John Behrens and Chong Ho Yu, 1995
  http//seamonkey.ed.asu.edu/behrens/asu/reports/c
  ompre/comp1.html
• Feinberg, S. E. Graphical methods in statistics.
  American Statisticians, 33, 165-178, 1979
• Friendly, Michael, Gallery of Data Visualization.
  http//www.math.yorku.ca/SCS/Gallery
• scan of Minards graph from Tufte 1983
• multivariate means comparison
• Wegman, Edward J. and Luo, Qiang. High
  Dimensional Clustering Using Parallel Coordinates
  and the Grand Tour., Conference of the German
  Classification Society, Freiberg, Germany, 1996.
  http//galaxy.gmu.edu/papers/inter96.html
• Cook, Dennis R and Weisberg, Sanford. An
  Introduction to Regression Graphics, 1995.
  http//stat.umn.edu/rcode/node3.html
• Schall, Matthew. SPSS DIAMOND a visual
  exploratory data analysis tool. Perspective, 18
  (2), 1995. http//www.spss.com/cool/papers/diamon
  dw.html
• Marchette, David. An Investigation of Chernoff
  Faces for High Dimensional Data Exploration.
  http//farside.nswc.navy.mil/CSI803/Dave/chern.htm
  l
• Chernoff, H. The use of Faces to Represent
  Points in k-Dimensional Space Graphically.
  Journal of the American Statistical Association,
  68, 361-368, 1973.

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Next Time Brushing and Linking

• An interactive technique
• Brushing
• pick out some points from one viewpoint
• see how this effects other viewpoints
• (Cleveland scatterplot matrix example)
• Graphs must be linked together

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Brushing and Linking Systems

• VISAGE Roth et. al
• Attribute Explorer Tweedie et. al
• SpotFire (IVEE) Ahlberg et. al