#26 La data visualisation pour la data science (et les data scientists)

Deﬁnitions [De]coding Howto ? Rules Perception Before/After Cases So what ? Références
Data Visualization for Data
Scientists
Christophe Bontemps
Toulouse School of Economics, INRA
@Xtophe_Bontemps

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MERCI À dream-team DE TDS

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THE “VISUAL PERCEPTION” OF A GRAPHIC
What do you see ?
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Some X variable
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Some points (N = 500 )

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THE “VISUAL PERCEPTION” OF A GRAPHIC
And here, what do you see ?
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Some X variable
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Some other points (N = 500 )

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“VISUAL PERCEPTION” AS A STATISTICAL TEST
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“ The human eye acts is a broad feature detector and general
statistical test”. Buja et al. (2009)

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Test : H0 : {There is "nothing" } = {No relation}

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Test : H0 : {There is "nothing" } = {No relation}
H1 : { There is "something" } = {There is some relation
(Correlation, linearity, heterogeneity, groups..) }

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[- WHAT IS DATA VISUALISATION ? -]
For Tukey (1977) “The greatest value of a picture is when it
forces us to notice what we never expected to see”

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Cleveland (1994) says that “graphical methods and techniques
are powerful tools for showing the structure of data”

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Bertin (1970) (translated in Bertin (1983)) deﬁnes it as a
"visual language" and, as such, with a semiology, i.e. with a
theory of the functions of signs and symbols.

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Bertin (1970) (translated in Bertin (1983)) deﬁnes it as a
"visual language" and, as such, with a semiology, i.e. with a
theory of the functions of signs and symbols.
Tufte (2001) “Graphics are instruments for reasoning about
quantitative information”

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GOALS OF DATA VISUALISATION
Data visualisation serves at least two main purposes
Data exploration
Graphs as visual tests, comparisons → short time to built
and to read

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Data exploration
and to read
Data representation
Summaries, comparisons, storytelling → long time to
build, short time to read

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Data exploration
and to read
Data representation
Summaries, comparisons, storytelling → long time to
build, short time to read
The problem is that :
“ Communicating implies simpliﬁcation
data exploration implies exhaustivity”

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THE BIG PICTURE : FROM "DATA TO VIZ"

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THE BIG PICTURE : FROM "VIZ TO DATA"

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[- DECODING VISUAL INFORMATION -]

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GRAPHICS IMMEDIATE TO UNDERSTAND
FIGURE – Where do people run in Paris
source : (N. Yau)
http://flowingdata.com/2014/02/05/where-people-run/

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GRAPHICS IMMEDIATE TO UNDERSTAND
FIGURE – Climate forecast uncertainty (S. Planton)

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GRAPHICS THAT NEED EXPLANATIONS :
FIGURE – How people spend their days (NYT).

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[- MISTAKES ! -]
Source : New Yorker

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USUAL MISTAKES
FIGURE – (source Wikipedia)

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USUAL MISTAKES : TRUNCATED GRAPH (ZERO AXIS)
FIGURE – (source Wikipedia)

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USUAL MISTAKES
FIGURE – Are you looking at the right thing ?

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USUAL MISTAKES : LIMITED SCOPE
FIGURE – Are you looking at the right thing ?
from Flowing data

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USUAL MISTAKES
FIGURE – Percentage of student starting and completing a “step” in
MOOC
Source : My 2017’ students (Jan & Mohamed), but also recent researchers’
presentations

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USUAL MISTAKES : PIE CHARTS

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USUAL MISTAKES : PIE CHARTS
Source https://twitter.com/freakonometrics/status/
612742330160951296

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USUAL MISTAKES : STACKED BARS

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USUAL MISTAKES : LEGITIMATE COMPARISON
IMPOSSIBLE !
FIGURE – from Dix and Ellis (1998) example

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VERY USUAL “Mistake”...
FIGURE – Major Cause of Worker Disability (1975-2010) (J. Schwabish,
2014).

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LEGITIMATE QUESTIONS :
What is the highest value observed ? When was it ?

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In 2010, what is the major cause of disability ?

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Is cancer (red curve) increasing over the period ?

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In the recent years, which causes have increased
(decreased) the most ?

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· · ·

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· · ·
You do not remember a damn thing of this graph !

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VERY USUAL “Mistake” : SMALL MULTIPLES
FIGURE – Major Cause of Disability - 1975-2010 (J. Schwabish, 2014).

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VERY USUAL “Mistake” II...

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What do you see here ?

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Easier to see the trend of each curve...

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Easier to see the trend of each curve...
Idea shared by Gelman (2004) and Munzner (2014)

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USUAL “Mistakes” : RADAR PLOTS
How to represent many characteristics on a single graph ?
http://data.visualisation.free.fr/Blog/
Why-you-should-never-use-radar-plots.nb.html

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USUAL “Mistakes” : BEWARE OF RADAR PLOTS
Representation (areas) change with axis order !
http://data.visualisation.free.fr/Blog/
Why-you-should-never-use-radar-plots.nb.html

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[- WHY CODING ? -]
If decoding is hard, why coding ?

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GRAPHICS reveal DATA : ANSCOMBE (1973) QUARTET
We use here 4 couples of random variables : (X1, Y1), (X2, Y2)
(X3, Y3) and (X4, Y4). All four data sets have the same
descriptive statistics.
Xs Mean Std. Dev. Ys Mean Std. Dev. corr(Xi, Yi) N
X1 9 3.32 Y1 7.5 2.03 0.8164 11
X2 9 3.32 Y2 7.5 2.03 0.8162 11
X3 9 3.32 Y3 7.5 2.03 0.8163 11
X4 9 3.32 Y4 7.5 2.03 0.8165 11

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ANSCOMBE (1973) QUARTET
All four data sets are described by the same linear model
(Yi = α + βXi + i), revealing apparently the same
relationships :
Dependent variable :
Y1
Y2
Y3
Y4
Regressed on :
Xi
, i=1,...,4
0.500 ∗∗∗ 0.500∗∗∗ 0.500∗∗∗ 0.500∗∗∗
Constant 3.000∗∗ 3.001∗∗ 3.002∗∗ 3.002∗∗
R2 0.667 0.666 0.666 0.667
Resid Std. Error 1.237 1.237 1.236 1.236
F Statistic 17.990∗∗∗ 17.966∗∗∗ 17.972∗∗∗ 18.003∗∗∗
Note : Data from Anscombe (1973). ∗ p <0.1 ; ∗∗ p < 0.05 ; ∗∗∗ p < 0.01

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A simple scatter plot (regression overlaid) shows something
very different.
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x1
y1
Regression of Y1 on X1 (with constant)
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y2
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y3
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NP : Plots of the residuals shows also same differences
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Fitted values
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Residual vs Fitted Plot
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[- RULES OF THUMB -]
“There are no “good” nor “bad” graphics (...), there are graphics
answering legitimate questions and graphics that do not answer
question at all ” Bertin (1970)
It is easy to criticize ... but are there some rules ?

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COMPARISON IS DIFFICULT
Yes ! there are some basic rules :
Compare what is comparable → statistics

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Use comparable elements → data visualisation

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And many people have already worked on that !

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Jacques Bertin

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Jacques Bertin
Edward Tufte

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Jacques Bertin
Edward Tufte
Tuckey, Cleveland, .....

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FUNDAMENTAL QUESTIONS (CHEN ET AL. (2007))
What to Whom, How and Why ?
A graphic may be linked to three pieces of text : its caption, a
headline and an article it accompanies. → should be consistent
and complement each other.

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Show or explore data ?
Different purpose, different comparisons, different requirements !

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Choice of Graphical form ?
Choice depends on the type of data to be displayed (e.g.
univariate continuous data, bivariate categorical data, etc..) and
on what is to be shown, what is tested (compared).

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Choice of Graphical form ?
Choice depends on the type of data to be displayed (e.g.
univariate continuous data, bivariate categorical data, etc..) and
on what is to be shown, what is tested (compared).
Unique solution ?
There is not always a unique optimal choice → alternatives can
be equally good or good in different ways, emphasizing different
aspects of the same data.

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[RULES :] EDWARD R. TUFTE’S
In his seminal book, Tufte (2001) propose some principles for
displaying quantitative information.
Data : Above all, show the data

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Question : Induce the viewer to think about the substance
rather than about methodology, graphic design. Encourage the
eye to compare different piece of data.

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Data-ink ratio : Maximize the ink-data ratio. Erase all non
data ink, Erase redundant information

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Integrity : Avoid distorting what the data have to say

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General to speciﬁc : Reveal the data at different levels of
detail (from broad picture to ﬁne structure)

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General to speciﬁc : Reveal the data at different levels of
detail (from broad picture to ﬁne structure)
Context : Graphical display should be closely integrated with
the statistical and verbal descriptions of the data set.

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PRACTICAL EXAMPLE : DATA-INK RATIO
Let’s start with a classical graph (R default - Boxplot )
g1 g2 g3 g4 g5
98 100 102 104 106 108 110 112
Groupe
Response
FIGURE – Distribution of a continuous variable on 4 groups

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ERASE ALL NON DATA INK
Groupe
Response
1 2 3 4 5
98 100 102 104 106 108 110 112

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ERASE ALL REDUNDANT !
Groupe
Response
1 2 3 4 5
98 100 102 104 106 108 110 112

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GOING FURTHER...
Groupe
Response
1 2 3 4 5
98 100 102 104 106 108 110 112

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AND SHOW THE DATA...
Groupe
Response
101.0
100.0
101.0
103.8
109.1
1 2 3 4 5

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HAVE WE LOST SOMETHING ?
g1 g2 g3 g4 g5
98 100 102 104 106 108 110 112
Groupe
Response
Groupe
Response
101.0
100.0
101.0
103.8
109.1
1 2 3 4 5
Did you noticed that group 1 and group 3 had the same median
(101.0) ? see the ggplot theme + theme_tufte()

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PRACTICAL EXAMPLE : INTEGRITY (THE LIE FACTOR)
LieFactor =
Size of effect shown in graphic
Size of effect in data
(1)
A Lie Factor = 1 indicates a substantial distortion
FIGURE – Fuel economy standards. (E. Tufte - from NY Times 1978)

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FIGURE – Fuel economy standards (revisited)
The "18 mpg" line measures 1.5 cm (in 1978) ; the "27,5 mpg"
measures 13 cm (in 1985)
−→ Lie factor = 14.5% ! ! !

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PRACTICAL EXAMPLE : CONTEXT
In the next 2 minutes, you will design “the best way” to
compare two numbers
75and
37.
From S. Ortiz

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CONTEXT MATTERS !
Solutions proposed by S. Ortiz

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CONTEXT MATTERS (FOLLOW-UP)
What are the problems you’ve encountered ?

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Context ?

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Context ?
Audience ?

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Context ?
Audience ?
What to compare ?

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Context ?
Audience ?
What to compare ?
Units ?

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Context ?
Audience ?
What to compare ?
Units ?
Multiple solutions ?

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[RULES :] BERTIN’S APPROACH (A VISUAL
LANGUAGE)
If graphs are used to communicate, it is a form of language.
Any language has a grammar, “words” and logic. Let us study
the science that deals with signs or sign language : “The
Semiology”.
TABLE – Bertin’s deﬁnition of 8 visual variables
Position (x, y)
Size
Value
Texture
Colour
Orientation
Shape

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SHAPE IS NOT SUITABLE FOR PROPORTIONALITY
Price of land in the East of France Bertin (1970)

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SIZE IS SUITABLE FOR PROPORTIONALITY
Price of land in the East of France Bertin (1970)

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WHAT ELSE ?
Is color suitable for
proportionality ?

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A NOTE ON COLORS
“Colors” are not suited for ordering nor for proportionality !
Try putting the following hues in order from low to high.

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A NOTE ON COLORS
These colors are easy to order from low to high.
Few (2008) provides meaningful solutions for choosing palettes
of colors, for example for heatmaps.
See also the ggplot theme theme_few()

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[RULES :] CLEVELAND-MCGILL

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THE CLEVELAND-MCGILL EFFECT

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THE CLEVELAND-MCGILL EFFECT
From Cleveland and McGill (1984)

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WEBER’S LAW AND FRAMED BOXES

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WEBER’S LAW AND FRAMED BOXES
From Cleveland and McGill (1984)

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[RULES :] ACCESSIBILITY
Normal →
Color-blind →

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[- PERCEPTION -]
//
Source :
http://flowingdata.com/2014/06/25/duck-vs-rabbit-plot/

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“PREATTENTIVE” VARIABLES
How many "3" in that sequence ? (from Ware (2012))

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AND NOW...
Find the red dot !

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TEST : FIND THE RED DOT !

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HARDER : IS THERE A "STRANGER" ?

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THAT WASN’T EASY
Preattentive concept, Treisman (1985)
Some visual elements or patterns are detected immediately
But there may be interferences (colour and form)
Very useful (detection, explanatory and presentation)
Helpful to highlight a message !

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TOO MUCH VARIATION DOESN’T HELP
From Ware (2012)

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MOST PREATTENTIVE VISUAL VARIABLES
From Ware (2012)

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[- BEFORE/AFTER -]
Source : Emma Rathbone - The New Yorker

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BEFORE (SCHWABISH - JEP, 2014)
FIGURE – An Unbalanced Chart - Original

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AFTER (SCHWABISH - JEP, 2014)
FIGURE – An Unbalanced Chart - Revised

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BEFORE (SCHWABISH - JEP, 2014)
FIGURE – A Clutterplot Example - Original

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AFTER (SCHWABISH - JEP, 2014)
FIGURE – A Clutterplot Example - Revised

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BEFORE - NETWORK EXAMPLE
Victor Hugo’s characters network (Les Miserables).

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ALTERNATIVE : ADJACENT MATRIX PLOT
An adjacency matrix, where each cell ij represents an edge from vertex i to
vertex j.

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ALTERNATIVE : SORTED ADJACENT MATRIX PLOT

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ALTERNATIVE : ARC DIAGRAM PLOT
FromGaston Sanchez

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ALTERNATIVE : VERTICAL ARC DIAGRAM PLOT

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BEFORE - STUDENTS GRADES IN 4 COURSES
Source Munzner (2014)

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AFTER - STUDENTS GRADES IN 4 COURSES
Source Munzner (2014)

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BEFORE : US AIRLINES MAP (C. HURTER)
Source Christophe Hurter

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AFTER : BUNDLING THE NETWORK (C. HURTER)
To simplify the understanding, researcher propose bundling
techniques. 1
1. To bundle : to tie or gather things together

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AFTER : BUNDLING IN NETWORKS (C. HURTER)
Edges get closer and density gets sharper :

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BUNDLING IN NETWORKS (C. HURTER)
Edges get even closer and density gets even sharper :

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BUNDLING IN NETWORKS (C. HURTER)
At the end of the day...one can see through darkness !

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CASE STUDIES

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CASE 1 : FUNNEL DATA ANALYSIS
Original data are percent of users in funnel data stages, or
gates :
Each stage represents some portion of the previous stage.
Source : www.storytellingwithdata.com

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Original data observed for 4 regions of the world

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... and for 3 cohorts (Q1, Q2 & Q3)

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Identify the interesting feature : What comparisons ?

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By cohort

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Remove superﬂuous information (Tufte’s rule)

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Compare cohorts trends

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Relabel the graphic

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Make comparison& visual choices (reference line)

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Provide insights

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Add color, context & analysis

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CASE 1 : BEFORE/AFTER
Source : www.storytellingwithdata.com

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CASE 2 : WHAT’S THE GOOD POINT SIZE ?
FIGURE – Sample size = 500, point size = 3

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FIGURE – With Transparency ! (Sample size = 500, point size = 13)

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FIGURE – Context matters ! (Sample size = 500, point size = 13)

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CASE 3 : SEARCHING FOR LEARNERS IN A MOOC
How learners behave during the course ?

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Learner’s "activity" over time /space

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The MOOC’s stucture :
FIGURE – The MOOC is made of 60 different steps (ressources)

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The MOOC’s stucture :
FIGURE – The MOOC is made of 60 different steps (ressources)
Learners may pick whatever step, whenever they want.

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Basic graphic # 1 : Barplot (stacked)
4.11
4.10
4.9
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4.1
3.21
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0 1000 2000 3000
Learners
Step
Completed Visited but not completed Comments
Activity per step

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Basic graphic # 2 : Heatmap
FIGURE – Heatmap showing activity over time

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Idea # 1 : Visualize steps visited over time (1 line = 1 learner)
FIGURE – How to visualize “Trajectories” over time ?

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Too many starting points and trajectories !
FIGURE – How to visualize “Trajectories” over time ?

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Idea # 2 : Align starting points ! Change time for clicks sequence
FIGURE – “Trajectories” as a sequence of “clicks”

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Steps vs clicks sequence should reveal = patterns
FIGURE – “Trajectories” as a sequence of “clicks”

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Steps vs clicks sequence should reveal = patterns
FIGURE – “trajectories” as a sequence of “clicks”

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Should work with many lines (many learners)
FIGURE – “trajectories” as a sequence of “clicks”

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Back to R.....
FIGURE – First try : Each line is a learner’s path

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FIGURE – Trick one : Apply transparency and grey lines

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FIGURE – Trick two : Tiny lines and "jitter"

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FIGURE – Trick three : Colored lines, "jitter" and simple labels

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FIGURE – Trick four : Add context (analysis)

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WHAT TO REMEMBER
From the viewer“data visualisation” are implicitly or explicitly
comparisons or even tests (in the statistical sense)
Graphics should help questioning

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WHAT TO REMEMBER
They should provide elements, to answer (data at least)

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WHAT TO REMEMBER
They should provide elements, to answer (data at least)
If the question implies comparison, they should truthfully
show the comparison

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WHAT TO REMEMBER : THERE ARE RULES
Data visualisation is a visual language, so there are :
Elements of language

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Rules of use (spelling)

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Rules of use (spelling)
Grammar

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THE TRUTH DOES NOT LIVE IN 2D
The “truth”....

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GRAPHS I LIKE
Visualizing thousands of runners (A. Ottenheimer)

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GRAPHS I LIKE
Atlas of Places (Muriz Djurdjevic & Thomas Paturet)

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GRAPHS I LIKE
Experiments in Time-Distance map (Kohei Suguira)

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REFERENCES I
Anscombe, F. J. (1973). Graphs in statistical analysis. The American
Statistician, 27(1) :17–21.
Bertin, J. (1970). La graphique. Communications, 15(1) :169–185.

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REFERENCES II
Bertin, J. (1983). Semiology of graphics, translation from sémilogie graphique
(1967).
Buja, A., Cook, D., Hofmann, H., Lawrence, M., Lee, E.-K., Swayne, D. F., and
Wickham, H. (2009). Statistical inference for exploratory data analysis and
model diagnostics. Philosophical Transactions of the Royal Society of London
A : Mathematical, Physical and Engineering Sciences, 367(1906) :4361–4383.
Chen, C.-h., Härdle, W. K., and Unwin, A. (2007). Handbook of data
visualization. Springer Science & Business Media.
Cleveland, W. S. (1994). The Elements of Graphing Data. Hobart Press,
Summit : NJ, 2 edition.
Cleveland, W. S. and McGill, R. (1984). Graphical perception : Theory,
experimentation, and application to the development of graphical
methods. Journal of the American Statistical Association, 79(387) :531–554.
Dix, A. and Ellis, G. (1998). Starting simple - adding value to static
visualisation through simple interaction. In Eds. T. Catarci, M.
F. Costabile, G. S. and Tarantino, L., editors, Proceedings of Advanced Visual
Interfaces, pages 124–134. L’Aquila, Italy, ACM Press.

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REFERENCES III
Few, S. (2008). Practical rules for using color in charts. Visual Business
Intelligence Newsletter, (11).
Gelman, A. (2004). Exploratory data analysis for complex models. Journal of
Computational and Graphical Statistics, 13(4).
Munzner, T. (2014). Visualization Analysis and Design. AK Peters Visualization
Series. A K Peters/CRC Press, 1 edition.
Treisman, A. (1985). Preattentive processing in vision. Computer Vision,
Graphics, and Image Processing, 31(2) :156–177.
Tufte, E. R. (2001). The Visual Display of Quantitative Information. Graphics
Press, 2 edition.
Tukey, J. W. (1977). Exploratory data analysis. Reading, Mass.
Ware, C. (2012). Information visualization : perception for design. Elsevier.

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STAY IN TOUCH !
My website Data.visualisation.free.fr
@Xtophe_Bontemps

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#26 La data visualisation pour la data science (et les data scientists)

#26 La data visualisation pour la data science (et les data scientists)

Toulouse Data Science

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