1. ICS 278: Data Mining Exploratory Data Analysis and Visualization
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

2. Lecture 4 Project proposals due next Thursday Today’s lecture
Exploratory Data Analysis and Visualization
Summary statistics
1 and 2 dimensional data visualization
Higher dimensional visualization
Examples of complex visualization
Reading: Chapter 3 in the text
Note: slides at end of last lecture on covariance, Mahalanobis distance, etc, will be revisited in next lecture
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

3. Exploratory Data Analysis (EDA)
get a general sense of the data
interactive and visual
(cleverly/creatively) exploit human visual power to see patterns
1 to 5 dimensions (e.g. spatial, color, time, sound)
e.g. plot raw data/statistics, reduce dimensions as needed
data-driven (model-free)
especially useful in early stages of data mining
detect outliers (e.g. assess data quality)
test assumptions (e.g. normal distributions or skewed?)
identify useful raw data & transforms (e.g. log(x))
Bottom line: it is always well worth looking at your data!
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

4. Summary Statistics not visual sample statistics of data X
mean:  = i Xi / n {  minimizes i (Xi - )2 }
mode: most common value in X
median: X=sort(X), median = Xn/2 (half below, half above)
quartiles of sorted X: Q1 value = X0.25n , Q3 value = X0.75 n
interquartile range: value(Q3) - value(Q1)
range: max(X) - min(X) = Xn - X1
variance: 2 = i (Xi - )2 / n
skewness: i (Xi - )3 / [ (i (Xi - )2)3/2 ]
zero if symmetric; right-skewed more common (e.g. you v. Bill Gates)
number of distinct values for a variable (see unique.m in MATLAB)
Note: all of these are estimates based on the sample at hand – they may be different from the “true” values (e.g., median age in US).
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

5. Exploratory Data Analysis
Tools for Displaying Single Variables
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

6. Histogram
Most common form: split data range into equal-sized bins Then for each bin, count the number of points from the data set that fall into the bin.
Vertical axis: Frequency (i.e., counts for each bin)
Horizontal axis: Response variable
The histogram graphically shows the following:
center (i.e., the location) of the data;
spread (i.e., the scale) of the data;
skewness of the data;
presence of outliers; and
presence of multiple modes in the data.
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

7. Issues with Histograms
For small data sets, histograms can be misleading. Small changes in the data or to the bucket boundaries can result in very different histograms.
Interactive bin-width example (online applet)
For large data sets, histograms can be quite effective at illustrating general properties of the distribution.
Can smooth histogram using a variety of techniques
E.g., kernel density estimation (pages in text)
Histograms effectively only work with 1 variable at a time
Difficult to extend to 2 dimensions, not possible for >2
So histograms tell us nothing about the relationships among variables
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

8. Histogram Example
classical bell-shaped, symmetric histogram with most of the frequency counts bunched in the middle and with the counts dying off out in the tails. From a physical science/engineering point of view, the Normal/Gaussian distribution often occurs in nature (due in part to the central limit theorem).
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

9. ZipCode Data: Population
K = 50
K = 500
K = 50
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

10. ZipCode Data: Population
MATLAB code: X = zipcode_data(:,2) % second column from zipcode array histogram(X, 50) % histogram of X with 50 bins
histogram(X, 500) % 500 bins index = X < 5000; % identify X values lower than 5000
histogram(X(index),50) % now plot just these X values
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

11. Histogram Detecting Outlier (Missing Data)
blood pressure = 0 ?
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

12. Right Skewness Example: Credit Card Usage
similarly right-skewed are
Power law distributions
(Pi ~ 1/ia, where a >= 1)
e.g. for a = 1 we have “Zipf’s law”
For word frequencies in text
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

13. Box (and Whisker) Plots: Pima Indians Data
all data
outside
whiskers
Q3-Q1
box contains middle 50% of data
up to
1.5 x
Q3-Q1
(or shorter,
if no data
that far
above Q3) Q2
(median)
healthy
diabetic
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

14. Time Series Example 1 annual fees introduced in UK
(many users cutback to 1 credit card)
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

15. summer bifurcations in air travel
Time Series Example 2
summer bifurcations in air travel
(favor early/late)
summer
peaks
steady growth
trend
New Year bumps
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

16. unexpected pattern (steps),
Time-Series Example 3
mean weight vs mean age
for 10k control group
Scotland experiment:
“ milk in kid diet  better health” ?
20,000 kids:
5k raw, 5k pasteurize,
10k control (no supplement)
Possible explanations:
Grow less early in year than later?
No steps in height plots; so why
height  uniformly, weight  spurts?
Kids weighed in clothes: summer garb lighter than winter?
Would expect smooth weight growth plot.
Visually reveals
unexpected pattern (steps),
not apparent from raw data table.
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

17. Non-Stationarity Stationarity: Examples:
(loose definition)
A probability distribution p (x | t) is stationary with respect to t if
p (x | t ) = p (x) for all t,
where x is the set of variables of interest, and
t is some other varying quantity (e.g., usually t = time, but could represent spatial information, group information, etc)
Examples:
p(customer demographics today) = p(customer demographics next month)?
p(weights in Scotland) = p(weights in US) ?
p(income of customers in Bank 1) = p(income of customers in Bank 2)?
Non-stationarity is common in real data sets
Solutions?
Model stationarity (e.g., increasing trend over time) and extrapolate
Build model only on most recent/most similar data
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

18. Exploratory Data Analysis
Tools for Displaying Pairs of Variables
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

19. 2D Scatter Plots standard tool to display relation between 2 variables
e.g. y-axis = response, x-axis = suspected indicator
useful to answer:
x,y related? no
linearly
nonlinearly
variance(y) depend on x?
outliers present?
MATLAB:
plot(X(1,:),X(2,:),’.’);
credit card repayment: low-low, high-high
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

20. Scatter Plot: No apparent relationship
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

21. Scatter Plot: Linear relationship
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

22. Scatter Plot: Quadratic relationship
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

23. Scatter plot: Homoscedastic
Variation of Y Does Not Depend on X
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

24. Scatter plot: Heteroscedastic
variation in Y differs depending on the value of X
e.g., Y = annual tax paid, X = income
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

25. (from US Zip code data: each point = 1 Zip code) units = dollars
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

26. Problems with Scatter Plots of Large Data
appears: later apps older; reality: downward slope (more apps, more variance)
96,000 bank loan applicants
scatter plot degrades into black smudge ...
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

27. Contour Plots Can Help recall: (same 96,000 bank loan apps as before)
shows variance(y)  with x 
is indeed due to horizontal
skew in density
unimodal
skewed 
skewed 
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

28. Problems with Scatter Plots of Large Data
# weeks credit card buys gas vs groceries
(10,000 customers)
actual correlation (0.48) higher than appears (overprinting)
also demands explanation
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

29. A simple data set
Data X Y
Anscombe, Francis (1973), Graphs in Statistical Analysis,
The American Statistician, pp
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

30. A simple data set
Data X Y
Summary Statistics
N = 11 Mean of X = 9.0 Mean of Y = 7.5 Intercept = 3 Slope = 0.5 Residual standard deviation = Correlation = 0.816
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

31. A simple data set
Data X Y
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

32. 3 more data sets
X2 Y X3 Y X Y4
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

33. Summary Statistics Summary Statistics of Data Set 2
N = 11 Mean of X = 9.0 Mean of Y = 7.5 Intercept = 3 Slope = 0.5 Residual standard deviation = Correlation = 0.816
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

34. Summary Statistics Summary Statistics of Data Set 2
N = 11 Mean of X = 9.0 Mean of Y = 7.5 Intercept = 3 Slope = 0.5 Residual standard deviation = Correlation = 0.816
Summary Statistics of Data Set 3
N = 11 Mean of X = 9.0 Mean of Y = 7.5 Intercept = 3 Slope = 0.5 Residual standard deviation = Correlation = 0.816
Summary Statistics of Data Set 4
N = 11 Mean of X = 9.0 Mean of Y = 7.5 Intercept = 3 Slope = 0.5 Residual standard deviation = Correlation = 0.816
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

35. Visualization really helps!
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

36. Exploratory Data Analysis
Tools for Displaying More than 2 Variables
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

37. Multivariate Visualization
Multivariate -> multiple variables
2 variables: scatter plots, etc
3 variables:
3-dimensional plots
Look impressive, but often not used
Can be cognitively challenging to interpret
Alternatives: overlay color-coding (e.g., categorical data) on 2d scatter plot
4 variables:
3d with color or time
Can be effective in certain situations, but tricky
Higher dimensions
Generally difficult
Scatter plots, icon plots, parallel coordinates: all have weaknesses
Alternative: “map” data to lower dimensions, e.g., PCA or multidimensional scaling
Main problem: high-dimensional structure may not be apparent in low-dimensional views
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

38. Scatter Plot Matrix For interactive visualization
the concept of “linked
plots” is generally
useful
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

39. Trellis Plot Older Younger Male Female
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

40. Using Icons to Encode Information, e.g., Star Plots
Each star represents a single observation. Star plots are used to examine the relative values for a single data point
The star plot consists of a sequence of equi-angular spokes, called radii, with each spoke representing one of the variables.
Useful for small data sets with up to 10 or so variables
Limitations?
Small data sets, small dimensions
Ordering of variables may affect perception
1 Price
2 Mileage (MPG)
Repair Record (1 = Worst, 5 = Best)
Repair Record (1 = Worst, 5 = Best)
5 Headroom
6 Rear Seat Room
7 Trunk Space
8 Weight
9 Length
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

41. Chernoff’s Faces Chernoff faces applet more icon plots
described by ten facial characteristic parameters: head eccentricity, eye eccentricity, pupil size, eyebrow slant, nose size, mouth shape, eye spacing, eye size, mouth length and degree of mouth opening
Chernoff faces applet
more icon plots
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

42. Parallel Coordinates interactive “brushing” is useful
(epileptic seizure data from text)
1 (of n)
cases
dimensions
(possibly all p of them!)
often (re)ordered
to better distinguish
among interesting
subsets of n total cases
(this case is
a “brushed”
one, with a
darker line,
to standout
from the n-1
other cases)
interactive
“brushing” is useful
for seeing such distinctions
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

43. More elaborate parallel coordinates example (from E. Wegman, 1999).
12,000 bank customers with 8 variables
Additional “dependent” variable is profit (green for positive, red for negative)
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

44. Interactive “Grand Tour” Techniques
“Grand Tour” idea
Cycle continuously through multiple projections of the data
Cycles through all possible projections (depending on time constraints)
Projects can be 1, 2, or 3d typically (often 2d)
Can link with scatter plot matrices (see following example)
Asimov (1985)
e.g. XGOBI visualization package (available on the Web)
Example on following 2 slides
7dimensional physics data, color-coded by group, shown with
Standard scatter matrix
static snapshot of grand tour
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

45. Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

46. Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

47. as used in OLAP/databases
Example of displaying
4d categorical data, e.g.,
as used in OLAP/databases
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

48. Other aspects (not discussed)
Cognitive and human-factors aspects of visualization
In creating visualizations of data it is important to be aware of how the human brain perceives visual information
E.g., “Rules and principles of scientific data visualization”
Artistic aspects of visualization
Classic books by Edward Tufte:
Visualization of other data
2d, 3d, 4d “volume” data (fluid flow, brain images, etc)
Network/graph data
Issues: graph layout/drawing, issues of graph size
Many others…., e.g.,
CHI conference, etc
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

49. Visualization of weather states for Kenya Daily data from 20 year history clustered into 3 different weather “states” Mean image for each state - wind direction (arrows) - wind intensity (size of arrows) - rainfall (size of circles) - pressure (contours) S. Kirshner, A. Robertson, P. Smyth, 2004.
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

50. Summary of 189k newsgroups and 257M postings
Green = increase in postings in 2004 over 2003, red = decrease
Uses “treemap” technique. Details at
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

51. Time-line Visualization of Research Fronts
Time-line Visualization of Research Fronts (Morris et al, JASIST, 2003)
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

52. Interactive MultiTile Visualization
Interactive MultiTile Visualization (Falko Kuester’s HIPerWall system, Calit2, UCI)
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine

53. Summary EDA and Visualization Reading: Chapter 3 Next lecture:
Can be very useful for
data checking
getting a general sense of individual or pairs of variables
But…
do not necessarily reveal structure in high dimensions
Reading: Chapter 3
Next lecture:
projecting/mapping data from high dimensions to low dimensions
Data Mining Lectures Lecture on EDA and Visualization Padhraic Smyth, UC Irvine