Ethan Burns eaburns at cs.unh - eatoasts.appspot.com fileWhat are Plots For? Introduction Outline Why Do We Care About Plots? What are Plots ... Box Plots Grouped Box Plots Log Scales

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Understanding Your Data Through Plots

Ethan Burnseaburns at cs.unh.edu

September 13, 2012

Introduction

Introduction

■ Outline■ Why Do We CareAbout Plots?■ What are PlotsFor?

■ Tables of Data

■ Pictures of Data

■ More Tables

■ More Pictures

Distributions ofValues

Trends in Data

Simple Plotting Tool

Other Tools

2 / 37

Outline

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

3 / 37

■ Why use plots?

■ Different types of plots

■ Tools that I use

Why Do We Care About Plots?

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

4 / 37

Grad Students do Research:

■ Theoretical analysis

■ Experimental analysis—lots of data

What are Plots For?

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

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1. Understand behavior of new techniques

We need to see what the data is telling us

2. Demonstrate (to others) that new approaches work well

We want to convince others using our data

Clear, and obvious display of data

Tables of Data

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

6 / 37

Experiments generate lots of data

My data:

1 2 3 4 5 6 7 8

run 1: -2.47 0.75 2.96 13.57 16.65 26.18 36.32 50.98

run 2: -1.46 2.37 7.17 10.68 18.60 26.05 37.46 46.85

run 3: 1.40 1.86 6.00 5.95 15.37 28.78 38.20 47.01

run 4: 1.98 -0.23 1.13 4.70 16.27 25.89 34.31 48.83

run 5: 0.31 -1.90 4.56 5.52 17.41 25.69 33.86 47.33

Tables of Data

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

6 / 37

Experiments generate lots of data

My data:

1 2 3 4 5 6 7 8

run 1: -2.47 0.75 2.96 13.57 16.65 26.18 36.32 50.98

run 2: -1.46 2.37 7.17 10.68 18.60 26.05 37.46 46.85

run 3: 1.40 1.86 6.00 5.95 15.37 28.78 38.20 47.01

run 4: 1.98 -0.23 1.13 4.70 16.27 25.89 34.31 48.83

run 5: 0.31 -1.90 4.56 5.52 17.41 25.69 33.86 47.33

What is going on here?

Pictures of Data

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

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6420

40

20

0

run1

run0

run2

run3

run4

Now we can see what our data is telling us

More Tables

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

8 / 37

More Pictures

Introduction


■ Tables of Data


■ More Tables

■ More Pictures


Trends in Data


Other Tools

9 / 37

Distributions of Values

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing

■ Box Plots■ Grouped BoxPlots

■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

10 / 37

Histograms

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

11 / 37

Histograms show a distribution of values:

bytes in my .tex file

ASCII10050

frequency

300

200

100

0

Histograms

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

11 / 37

Histograms show a distribution of values:


ASCII10050

frequency

300

200

100

0

newline

and

tab space

punctuation

letters and

numbers

Can quickly show modes—areas of high frequency

2D Histograms: Heatmaps

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

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Heatmap

100500

100

50

0

Bin Width

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

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The width of bins can have a big impact on the histogram


ASCII10050

frequency

300

200

100

0

If bins are too big, information can be hidden

Bin Width

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

13 / 37



ASCII1000

frequency 2000

1000

0


Bin Width

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

13 / 37



ASCII2001000

frequency 2000

1000

0


Comparing distributions

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

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first 100 bytes in files

Byte values2001000

frequency

60

30

0

plot.tex

dict

/bin/ls

Box Plots

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

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fir st 100 bytes in files

ASCII

200

100

0

/bin /ls dict plot .t ex

Box Plots

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

15 / 37

fir st 100 bytes in files

ASCII

200

100

0

/bin /ls dict plot .t ex

3rd quartile

1st quartile

median

maximum

'minimum'

outside

points

Grouped Box Plots

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

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norm

alized reward

1

0.8

0.6

react h=80.2 damage

react h=80.4 damage

0.2 order

react h=80.2 damage

react h=80.4 damage

0.4 order

Log Scales

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

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Raw values

time (seconds)

100

50

IDA*

Log10 values

log10 tim

e (seconds)

2

1

0

-1

IDA*

log10 values can spread out data for visualization

Paired Data

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

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Unpaired Data

log10 tim

e (seconds)

2

1

0

-1

My IDA* Korf's IDA*

Paired Data

Factor of Korf's IDA* tim

e

1

0.9

0.8

My IDA*

Paired data—show instance-by-instance differences

Summary

Introduction


■ Histograms

■ Heatmap

■ Bin Width

■ Comparing


■ Log Scales

■ Paired Data

■ Summary

Trends in Data


Other Tools

19 / 37

■ Histograms easily show data distributions

◆ Careful when choosing bin widths

◆ Histograms are difficult to compare

■ Heatmaps are like histograms for 2D data

■ Box plots make comparing distributions easy

◆ Grouped box plots can help to show trends

■ Log scales can help spread out data for visualization

■ Paired data is more powerful

Trends in Data

Introduction


Trends in Data

■ Lines■ Lines and ErrorBars

■ Scatter Plots■ ConfidenceIntervals■ More ScatterPlots

■ Scatters and Lines■ More Logs andPaired Data

■ Summary


Other Tools

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Lines

Introduction


Trends in Data




■ Summary


Other Tools

21 / 37

3000

4000

5000

6000

7000

8000

9000

0 2 4 6 8 10 12 14

Thr

ough

put (

Meg

abits

/sec

ond)

Size (Megabytes)

iSER-Assisted WRITE commands (Size v.s. Throughput)

Kernel-space iSER-assisted iSCSI WRITEsUser-space iSER-assisted iSCSI WRITEs

Lines and Error Bars

Introduction


Trends in Data




■ Summary


Other Tools

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log10(sample size)63

fraction correct

0.9

0.6

0.3New

Previous

Scatter Plots

Introduction


Trends in Data




■ Summary


Other Tools

23 / 37

Korf 15

log10 CPU Time-3 -2 -1 0 1

Solu

tion

Len

gth

60

120

180

240

DeterministicRefine A* 10Refine A* 75Beam Search

wA* 1.5wA* 10

Confidence Intervals

Introduction


Trends in Data




■ Summary


Other Tools

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Korf 15

log10 CPU Time-3 -2 -1 0

Solu

tion

Len

gth

50

100

150

200 DeterministicRefine A* 10Refine A* 75Beam Search

wA* 1.5wA* 10

More Scatter Plots

Introduction


Trends in Data




■ Summary


Other Tools

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time200100

cost

2000

1000

time200100

cost

2000

1000

log10(nodes)1086

log10(predicted / actual)

2

1

0

-1

Previous

New

Scatters and Lines

Introduction


Trends in Data




■ Summary


Other Tools

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Scaling waypoints

log10 total wall time1.20.60

final sol cost

0.8

0.410.

20.

30.

40.

10.

20.

30.

40.

10.

20.

30.

40.

min

greedy

LP

More Logs and Paired Data

Introduction


Trends in Data




■ Summary


Other Tools

27 / 37


Introduction


Trends in Data




■ Summary


Other Tools

27 / 37

plat2d

log10 wf0-2-4-6

goal ach

ievement time

30000

20000

10000

0

speedy

bugsy

bugsy -hd

astar


Introduction


Trends in Data




■ Summary


Other Tools

27 / 37

plat2d

log10 wf0-2-4-6

log10 goal ach

ievement time

4

2

0

astar

speedy

bugsy -hd

bugsy


Introduction


Trends in Data




■ Summary


Other Tools

27 / 37

plat2d

log10 wf0-2-4-6

log10 factor of best goal ach

ievement time

1.6

0.8

0

astar

speedy

bugsy -hd

bugsy

Summary

Introduction


Trends in Data




■ Summary


Other Tools

28 / 37

■ Lines easily show trends in data

■ Scatter plots can show trends in points

■ Use confidence intervals—or some measure of variance

■ Logs can be helpful here too

■ Paired data is always better


Introduction


Trends in Data


■ What is It?

■ Why a New Tool?

■ Spread Sheets

■ Benefits of SPT

Other Tools

29 / 37

What is It?

Introduction


Trends in Data


■ What is It?

■ Why a New Tool?

■ Spread Sheets

■ Benefits of SPT

Other Tools

30 / 37

Simple Plotting Tool—SPThttp://www.cs.unh.edu/~eaburns/spt

■ An(other) open source plotting tool

■ Created by the UNH artificial intelligence group

■ Easy to create many useful types of plots

■ An Objective Caml API

■ A simple lisp-like input language

http://www.cs.unh.edu/~eaburns/spt

Why Make a New Plotting Tool?

Introduction


Trends in Data


■ What is It?

■ Why a New Tool?

■ Spread Sheets

■ Benefits of SPT

Other Tools

31 / 37

Spread sheets a lot of manual work

GNU plot is ugly (in my opinion, and Wheeler’s too)

Matplotlib better—still draws ticks inside and data on the axes

R not too bad!

Spread Sheets

Introduction


Trends in Data


■ What is It?

■ Why a New Tool?

■ Spread Sheets

■ Benefits of SPT

Other Tools

32 / 37

Benefits of SPT

Introduction


Trends in Data


■ What is It?

■ Why a New Tool?

■ Spread Sheets

■ Benefits of SPT

Other Tools

33 / 37

■ Professional quality plots (not cartoony)

◆ Greater data-ink ratio (Edward Tufte)

Axes do not box in the data

Not too many tick marks

◆ Axes are not drawn over the data

■ Very easy to make box plots

With confidence intervals

Grouped box plots too

■ Lines and scatters with 95% confidence intervals

■ Histograms and heatmaps from x,y(,z) tuples

Other Tools

Introduction


Trends in Data


Other Tools

■ Results Database

■ Alternatives

■ Plotinum

34 / 37

Results Database

Introduction


Trends in Data


Other Tools


■ Alternatives

■ Plotinum

35 / 37

I store my results in a simple database called RDB—ResultsDataBase (or is it Ruml DataBase?)

■ A simple file-system-based database

■ Easy to find data files given a set of key=value pairs

■ Has an OCaml API, a C++ API, and shell scriptingsupport

■ Simple data files: key=value, or key=multi-value pairs

■ Framework connecting RDB → OCaml → SPT

Other More Standard Alternatives

Introduction


Trends in Data


Other Tools


■ Alternatives

■ Plotinum

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■ MongoDB

■ CouchDB

■ SQLite

Plotinum: My Latest Plotting Tool

Introduction


Trends in Data


Other Tools


■ Alternatives

■ Plotinum

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■ Another-nother open source plotting tool

0 0.5 1

0

0.5

1

http://code.google.com/p/plotinum

■ Written in Go

golang.org, check it out!

■ Simpler, more flexible, and more extendable than SPT

...but, a little less complete at the moment

http://code.google.com/p/plotinum

Ethan Burns eaburns at cs.unh - eatoasts.appspot.com fileWhat are Plots For? Introduction Outline Why Do We Care About Plots? What are Plots ... Box Plots Grouped Box Plots Log Scales

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