IRDS: VisualizationCharles Sutton

University of Edinburgh

Why visualisation?

• Exploratory • What’s in the data? What’s wrong with it? • Today’s lecture.

• Presentation • Display results of algorithms for publication

• Engagement • Infographics from web sites, word clouds, etc

Summary Statistics

• Univariate • Mean • Median • Variance • Quantiles

• Multivariate • Correlation • Covariance

Histograms

4 6 8 10 12 14 16

020

60100

8 10 12 14 16 18 20

040

80120

skew multimodality

6 8 10 12 14

020

4060

80these three have same summary statistics!

Outliers in histograms

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

Histogram Detecting Outlier (Missing Data)

blood pressure = 0 ?

Blood pressure data set

[Source: Padhraic Smyth]UCI ML repository says no missing data

(well, for 20 years it did)

Class-Conditional Histograms

Alternative: Box plot

Positive (diabetes)

Negative

Blood Pressure

Freq

uenc

y

0 20 40 60 80 100

020

4060

80

Blood Pressure

Freq

uenc

y

0 20 40 60 80 100

050

100

150

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neg pos

020

4060

80100120

Diabetes?Pressure Median

Quartile

Quartile

Extreme data

Maybe for only 2 groups, graphs not necessary. For more visual comparisons, can be helpful.

Slight rant about bar charts

Here’s my boxplot

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neg pos

020

4060

80100120

Diabetes?

Pressure

Weka’s automatic visualisation

Bar charts often seem like a better idea than they are

Effect of bin size

0 10 20 30 40 500

1020

3040

5060

Effect of bin size

0 10 20 30 40 500

1020

3040

5060

0 10 20 30 40 50

05

1015

2025

3035

Effect of bin size

0 10 20 30 40 50

05

1015

2025

3035

0 10 20 30 40 500

510

1520

2530

More misleading histograms

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

ZipCode Data: Population

0 2 4 6 8 10 12

x 104

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2 4 6 8 10 12

x 104

0

100

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300

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0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

50

100

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[Source: Padhraic Smyth]Data: US Post Codes

Bivariate data

• Numerical summaries about linear dependence • Histograms sort of scale to 2-D but not really higher • More common to use scatter plots

Numerical bivariate summaries

Sample covariance:

Sample correlation:

⇢xy

=sxy

sx

sy

where as beforex̄ =

1

N

X

i

xi

ȳ =1

N

X

i

yi

s

x

=

s1

N � 1X

i

(xi

� x̄)

sy =

s1

N � 1X

i

(yi � ȳ)

Data are (x1, y1), (x2, y2), . . . (xN , yN )

s

xy

=1

N � 1

NX

i=1

(yi

� ȳ)(xi

� x̄)

Dangers of correlation

4 6 8 10 12 14

46

810

14

4 6 8 10 12 14

46

810

14

4 6 8 10 12 14

46

810

14

8 10 12 14 16 18

46

810

14

[Anscombe, 1973]

Scatterplots

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−3 −2 −1 0 1 2 3

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3

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1000 data points

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