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Visualization �and�Data Mining

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Outline

  • Graphical excellence and lie factor
  • Representing data in 1,2, and 3-D
  • Representing data in 4+ dimensions
    • Parallel coordinates
    • Scatterplots
    • Stick figures

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Visualization Role

  • Support interactive exploration
  • Help in result presentation
  • Disadvantage: requires human eyes
  • Can be misleading

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Bad Visualization: �Spreadsheet

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2,124

2003

2,121

2002

2,120

2001

2,105

2000

2,110

1999

Sales

Year

What is wrong with this graph?

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Bad Visualization: �Spreadsheet with misleading Y –axis

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2,124

2003

2,121

2002

2,120

2001

2,105

2000

2,110

1999

Sales

Year

Y-Axis scale gives WRONG

impression of big change

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Better Visualization

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2,124

2003

2,121

2002

2,120

2001

2,105

2000

2,110

1999

Sales

Year

Axis from 0 to 2000 scale gives

correct impression of small change

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Lie Factor

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Tufte requirement: 0.95<Lie Factor<1.05

(E.R. Tufte, “The Visual Display of Quantitative Information”, 2nd edition)

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Tufte’s Principles of �Graphical Excellence�

  • Give the viewer
    • the greatest number of ideas
    • in the shortest time
    • with the least ink in the smallest space.

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  • Tell the truth about the data!

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(E.R. Tufte, “The Visual Display of Quantitative Information”, 2nd edition)

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Visualization Methods

  • Visualizing in 1-D, 2-D and 3-D
    • well-known visualization methods
  • Visualizing more dimensions
    • Parallel Coordinates
    • Other ideas

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1-D (Univariate) Data

  • Representations

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7

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5

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3

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1

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0

20

Mean

low

high

Middle 50%

Tukey box plot

Histogram

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2-D (Bivariate) Data

  • Scatter plot, …

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price

mileage

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3-D Data (projection)

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price

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Lie Factor=14.8

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Lie Factor=14.8

(E.R. Tufte, “The Visual Display of Quantitative Information”, 2nd edition)

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3-D image �(requires 3-D blue and red glasses)

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Taken by Mars Rover Spirit, Jan 2004

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Visualizing in 4+ Dimensions

  • Scatterplots
  • Parallel Coordinates
  • Chernoff faces
  • Stick Figures
  • …

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Multiple Views

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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

A B C D E

1

2

3

4

Problem: does not show correlations

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Scatterplot Matrix

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Represent each possible

pair of variables in their

own 2-D scatterplot

(car data)

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Q: Useful for what?

A: linear correlations

(e.g. horsepower & weight)

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Q: Misses what?

A: multivariate effects

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Parallel Coordinates

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  • Encode variables along a horizontal row
  • Vertical line specifies values

Dataset in a Cartesian coordinates

Same dataset in parallel coordinates

Invented by

Alfred Inselberg

while at IBM, 1985

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Example: Visualizing Iris Data

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Iris setosa

Iris versicolor

Iris virginica

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Flower Parts

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Petal, a non-reproductive part of the flower

Sepal, a non-reproductive part of the flower

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Parallel Coordinates

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Sepal

Length

5.1

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Parallel Coordinates: 2 D

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Sepal

Length

5.1

Sepal

Width

3.5

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Parallel Coordinates: 4 D

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Sepal

Length

5.1

Sepal

Width

Petal

length

Petal

Width

3.5

1.4

0.2

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Parallel Visualization of Iris data

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5.1

3.5

1.4

0.2

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Parallel Visualization Summary

  • Each data point is a line
  • Similar points correspond to similar lines
  • Lines crossing over correspond to negatively correlated attributes
  • Interactive exploration and clustering

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  • Problems: order of axes, limit to ~20 dimensions

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Chernoff Faces

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Encode different variables’ values in characteristics

of human face

http://www.cs.uchicago.edu/~wiseman/chernoff/

http://hesketh.com/schampeo/projects/Faces/chernoff.html

Cute applets:

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Interactive Face

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Chernoff faces, example

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Stick Figures

  • Two variables are mapped to X, Y axes
  • Other variables are mapped to limb lengths and angles
  • Texture patterns can show data characteristics

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Stick figures, example

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census data showing

age, income, sex,

education, etc.

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Closed figures correspond to women and we can see more of them on the left.

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Note also a young woman with high income

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Visualization software

Free and Open-source

  • Ggobi
  • Xmdv

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  • Many more - see www.KDnuggets.com/software/visualization.html

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Visualization Summary

  • Many methods
  • Visualization is possible in more than 3-D
  • Aim for graphical excellence

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