Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 1 Graphing to visualize data Satish Raghunath [email protected] Shiv Kalyanaraman Google: “Shiv

Shivkumar KalyanaramanRensselaer Polytechnic Institute

1

Graphing to visualize data

Satish [email protected]

Shiv KalyanaramanGoogle: “Shiv RPI”

[email protected] http://www.ecse.rpi.edu/Homepages/shivkuma


2

Issues with graphing Types of graphs Examples of graph usage & what you get out of them

Art: how to choose what graph to use? Graphing Tools Pitfalls and mistakes in graphing Advanced: visualization In class work: reviewing graphing use in selected technical

papers

Overview


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Thoughts on Presentation Styles

Primary purpose: illustrate to help understand

“The goal of simulation is intuition, not numbers," - R.W. Hamming

Corollary: don’t dump data on the reader. Distill it into presentations that give insight instead…


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Descriptive Statistics

InvolvesCollecting DataPresenting DataCharacterizing DataUnderstanding

data: distill insights!

X = 30.5 SX = 30.5 S22 = 113 = 113

00

2525

5050

Q1Q1 Q2Q2 Q3Q3 Q4Q4

$$

Insights: Somewhat skewed Bell shape: perhaps a Poisson (distrn) would fit?

Statistics obtained from data


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To graph or not to graph

Use graphs whenTrends in data are not obvious It is hard to explain the X-Y relationship in

words Consider tables if

The number of data-points are smallReader might find exact value of data-points

useful


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Summary Table: Frequencies

1. Lists Categories & No. Elements in Category 2. Obtained by Tallying Responses in Category 3. May Show Frequencies (Counts), % or Both

Row Is Category

Tally:|||| |||||||| ||||

Major CountAccounting 130Economics 20Management 50Total 200


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Example Tables from Networking

SACK (Multiple Sources)

LT-TCP (Multiple Sources)


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What kind of graph?

Pie-charts to depict “fraction of a whole” Bar-charts when data-points few and table is not

suitable Line-plots when there are a lot of data-points Box-plots if statistical inference is drawn: shows

1st, 2nd, 3rd quartile for each point. Scatter-plots, 3-d plots only if necessary –

AVOID complex graphs


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Econ.10%

Mgmt.25%

Acct.65%

Pie Chart

1. Shows Breakdown of Quantity into Categories

2. Useful for Showing Relative Differences

3. Angle Size (360°) x (Percent)

Majors

(360°) (10%) = 36°

36°


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Pie Chart Networking Example

Source: http://www.caida.org/~bhuffake/papers/skitviz/


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Another eg: VPN Classification


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00 5050 100100 150150

Acct.Acct.

Econ.Econ.

Mgmt.Mgmt.

Bar Chart

Horizontal Horizontal Bars for Bars for Categorical Categorical VariablesVariables

Bar Length Bar Length Shows Shows Frequency Frequency or %or %

1/2 to 1 Bar 1/2 to 1 Bar WidthWidth

Equal Bar Equal Bar WidthsWidths

Zero PointZero Point

FrequencyFrequency

MajorMajor

Percent Used AlsoPercent Used Also


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Networking Example Bar Chart


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Example Analysis with Bar Charts

LT-TCP is able toreduce timeouts drasticallykeep the queue non-empty maximizing throughput and capacity utilization.minimize use of FEC to level needed


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00

11

22

33

44

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Histogram: for “distributions”

FrequencyFrequency

Relative Relative FrequencyFrequency

PercentPercent

00 1515 2525 3535 4545 5555

Lower BoundaryLower Boundary

Bars Bars TouchTouch

ClassClass Freq.Freq.15 but < 2515 but < 25 3325 but < 3525 but < 35 5535 but < 4535 but < 45 22

CountCount


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Recall: Real Example Histogram What is the fairness between TCP goodputs when we use different queuing

policies? What is the confidence interval around your estimates of mean file size? Note: “distribution” need not just be a probability/frequency distribution

FQ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 4 7 10 13 16 19 22 25 28 31Flow Number

Thro

ughp

ut(M

bps)

RED

0

1

2

3

4

5

6

7

8

9

10

1 4 7 10 13 16 19 22 25 28 31Flow Number

Thro

ughp

ut(M

bps)


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00 5050 100100 150150

Acct.Acct.

Econ.Econ.

Mgmt.Mgmt.

Dot Chart or Scatterplots

FrequencyFrequency

MajorMajor Line Length Line Length Shows Shows Frequency or %Frequency or %

Equal Equal SpacingSpacing

Like Like Horizontal Horizontal Bar ChartBar Chart

Percent Used AlsoPercent Used Also

Horizontal Horizontal Lines for Lines for Categorical Categorical VariablesVariables

Zero PointZero Point


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Scatter Plots


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Scatter plots with trends


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WiFi Analysis: Scatter Plots http://www.sigcomm.org/sigcomm2004/papers/p442-aguayo1111.pdf


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Line Charts:Example:

Comparative Performance

Note: also plots confidence intervals!


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Line Plots for Distributions: Example

Hop count and RTT distributions

Source: http://www.caida.org/~bhuffake/papers/skitviz/


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Recall: Distribution Shape

1. Describes How Data Are Distributed 2. Measures of Shape

Skew = Symmetry

Right-SkewedRight-SkewedLeft-SkewedLeft-Skewed SymmetricSymmetric

MeanMean = = MedianMedian = = ModeModeMeanMean MedianMedian ModeMode ModeMode MedianMedian MeanMean


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Box Plot

Graphical Display of Data Using5-Number Summary

MedianMedian

44 66 88 1010 1212

QQ33QQ11 XXlargestlargestXXsmallestsmallest


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3D Graphs Example Illustrates a complex parameter response surface ...


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3D Plots: N/w Example: Code Red Worm Analysis

http://www.prism.uvsq.fr/users/qst/Tomography/Articles_jmf/renesys_bgp_instabilities2001.pdf http://www.caida.org/outreach/isma/0112/talks/andyo/index.pdf http://www.renesys.com/resource_library/Renesys-NANOG23.pdf


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Contd…


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Tools: Gnuplot

To use with data-generating programs for repetitive plotting

E.g. generate the plot of throughput for every 1 hour interval in the last week.

http://www.gnuplot.info TIP: Export gnuplot plots as “.fig” file and edit it in

xfig for greater flexibility


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Tools: XmGrace

For more intricate details (e.g., creating error-bars, different shades for bar-charts); GUI-driven, very user friendly.

http://plasma-gate.weizmann.ac.il/Grace/ Exports images to EPS (good for LaTeX

documents), PNG (good for PowerPoint) etc. Can also run on Windows on top of Cygwin!


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Tools: MATLAB

For complex 3-d and other statistical plots like box-plots, scatter-plots and in general if enormous quantities of data is involved.

http://www.mathworks.com


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Tools: Excel Data Presentations

Open up Excel to a new Worksheet. Code a data set as below:

Blue 34

White 68

Red 25

Green 50 Explore simple data presentation possibilities…


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Graphs: things to watch out Purpose: illustrate entire time-series or response

distribution Label the x- and y-axis Check what units the x- and y-axes are in (not “goats” or

“sheep”!) Check if either scale is logarithmic (changes meaning) Check where is the origin (or zero point) for each axis! After understanding WHAT is being plotted, close your

eyes and ask: what will different patterns on this graph imply (relative

to what I want to understand)? See if the relative performance is over- or under-

emphasized (if two systems are being compared) Several examples in the Jain textbook


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Errors in Presenting Data

1. Using ‘Chart Junk’

2. No Relative Basis in Comparing Data Batches

3. Compressing the Vertical Axis

4. No Zero Point on the Vertical Axis


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‘Chart Junk’

Bad PresentationBad Presentation Good PresentationGood Presentation

1960: $1.001960: $1.00

1970: $1.601970: $1.60

1980: $3.101980: $3.10

1990: $3.801990: $3.80

Minimum WageMinimum Wage Minimum WageMinimum Wage

00

22

44

19601960 19701970 19801980 19901990

$$


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No Relative Basis

Good PresentationGood Presentation

A’s by ClassA’s by Class A’s by ClassA’s by Class

Bad PresentationBad Presentation

00

100100

200200

300300

FRFR SOSO JRJR SRSR

Freq.Freq.

0%0%

10%10%

20%20%

30%30%

FRFR SOSO JRJR SRSR

%%


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Compressing Vertical Axis


Quarterly SalesQuarterly Sales Quarterly SalesQuarterly Sales


00

2525

5050

Q1Q1 Q2Q2 Q3Q3 Q4Q4

$$

00

100100

200200

Q1Q1 Q2Q2 Q3Q3 Q4Q4

$$


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No Zero Point on Vertical Axis


Monthly SalesMonthly Sales Monthly SalesMonthly Sales


00

2020

4040

6060

JJ MM MM JJ SS NN

$$

3636

3939

4242

4545

JJ MM MM JJ SS NN

$$


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Graphing Practices: In pictures


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Graphing Practices…


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Graphing Practices…


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Graphing Practices….


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Checklist: In textbook


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More Complex Visualizations Internet topology aspects: CAIDA skitter project

http://www.caida.org/tools/measurement/skitter/visualizations.xml


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More…


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The End

Documents

Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 1 Graphing to visualize data Satish Raghunath [email protected] Shiv Kalyanaraman Google: “Shiv