A Overview of Information Visualization

Michael McGuffin, Ph.D.

Associate Professor Department of Software and IT Engineering

École de technologie supérieure (ETS) Montreal, Canada

http://profs.etsmtl.ca/mmcguffin/

SECTION1:Visualiza2onofmul2dimensionalmul2variate(MDMV)data,alsoknownastabulardataorrela2onaldata

Someelementarymath•  Giventwosets,adomain(example:R)andacodomain

(example:R),wecanformthecartesianproduit(R×R=R2)thatisthesetofallpossiblepairs(x,y)–  {wild,tame}×{dog,cat}={(wild,dog),(wild,cat),(tame,dog),(tame,cat)}–  A×B={(a,b)|aϵAandbϵB}–  A×B×C×D={(a,b,c,d)|aϵAandbϵBandcϵCanddϵD}

•  Arela0onisasubsetofacartesianproduct–  Example:theequa2onx=y2correspondstoasubsetofR2;

theinequa2onx<ycorrespondstoanothersubsetofR2

•  Arela2onisafunc0onifeachmemberxofthedomainhasatmostonecorrespondingmemberyinthecodomain–  x=y2isnotafunc2onbecause(4,2)and(4,-2)arebothmembersofthe

rela2ondefinedbytheequa2on

•  Onewaytorepresentarela2on(orafunc2on)istosimplyenumeratethepairsoftherela2oninatable

The function y = x^0.5: x y --- --- 0 0 1 1 4 2 9 3 ... The relation in a table in a relational database: Client_name Product_bought Price Date ... ------------- ----------------- ------- ------------ ----- Robert G. Trombone 500.00 2008 March 7 . Robert G. Partitions vol. 1 45.00 2008 March 7 . Lucie M. Flute 180.00 2007 Nov 11 . Cynthia S. Partitions vol. 2 40.00 2008 June 16 Jules T. Piano 6000.00 2008 Jan 10 Jules T. Partitions vol. 1 45.00 2008 Jan 13 ... A video or movie file: x y time red green blue --- --- ------- ------- ------ ------ 0 0 0 255 0 0 0 1 0 200 10 6 ... 0 0 0.1 255 50 100 0 1 0.1 255 200 190 ...

Examples of mathematical relations (i.e., multidimensional multivariate data). A relation is a subset of a cartesian product of two or more sets (example: a subset of R×R). In the examples here, each row is a tuple (member of the relation), and each column corresponds to a set within the cartesian product.

A video: x y time red green blue --- --- ------- ------- ------ ------ 0 0 0 255 0 0 0 1 0 200 10 6 ... 0 0 0.1 255 50 100 0 1 0.1 255 200 190 ...

Domains Independent variables

Dimensions Dimensions

Co-domains Dependant variables Variables (hence the term “MDMV”) Measures (database terminology)

Tuple, Multidimensional point, Vector, Row

Columns, Variables

Terminology

I’ll use the terms in bold

Output graphical representation: at most 3 spatial dimensions (often just 2), at most 1 temporal dimension (animation)

Tovisualizedata,weneedtochooseamapping

Input data: an arbitrary number of dimensions and measures

1dimension+1measure:barchart(orlinechart)

2measures:sca\erplot

2dimensions+1measure:heatmap

Red

Blue

Green

Avideo

[Gareth Daniel and Min Chen, 2003]

Fluidvisualiza2onWhich dimensions and measures would be involved in such data?

Chernofffaces(1973)(anexampleofa"glyph")

Advantage: better than text for getting an overall impression of the data, and for identifying interesting elements.

Disadvantage: the mapping from variables to faces has an effect on the salience of each variable.

Disadvantage (?): redundancy of symmetry of faces

http://kspark.kaist.ac.kr/Hum

an%20E

ngineering.files/Chernoff/life_in_LA

.jpg ht

tp://

map

mak

er.ru

tger

s.ed

u/35

5/C

hern

off_

face

.gif

Otherexamplesofglyphs

M. Ward (2002), “A Taxonomy of Glyph Placement Strategies for Multidimensional Data Visualization”, Information Visualization.

Otherexamplesofglyphs

Wittenbrink, Pang, Lodha (1996) “Glyphs for Visualizing Uncertainty in Vector Fields”, IEEE TVCG.

Candles2ckcharts

•  InventedbyHommaMunehisa(1724-1803),whoamassedafortunebytradingrice

•  Usedinthetechnicalanalysisoffinancialmarkets•  Glyphsthatshowsevolu2onover2me

http://goodasgoeldi.com/wordpress/2009/06/26/reading-a-candlestick-graph/

http://goodasgoeldi.com/wordpress/2009/06/26/reading-a-candlestick-graph/

http://goodasgoeldi.com/wordpress/2009/06/26/reading-a-candlestick-graph/

1 White candlestick 2 Black candlestick 3 Long lower shadow 4 Long upper shadow 5 Hammer 6 Inverted hammer 7 Spinning top white 8 Spinning top black 9 Doji 10 Long legged doji 11 Dragonfly doji 12 Gravestone doji 13 Marubozu white 14 Marubozu black

http://en.wikipedia.org/wiki/Candlestick_chart

Interac2vePresenta2onfromtheUN(UnitedNa2onsDevelopmentProgramme,HumanDevelopmentReport)

See also Hans Rosling’s presentations on http://www.ted.com

Notice that the “points” here are glyphs, each with a radius and a color.

Tableau:sohwareforvisualizingdatabases(Mackinlayetal.2007,tableausohware.com)

x

y

b

a

x

yx

y

x

y

Rows: b, y

Columns: a, x

This is called dimensional stacking, and has been used in previous work before Tableau, but Tableau is a really nice implementation of it, and a successful commercial product.

Tableau

•  Formoreinforma2on:h\p://www.tableausohware.com/products/tourh\p://www.tableausohware.com/products/desktop/demo

Kindsofvariables•  Quan2ta2ve(orcon2nuousormetric)

–  Examples:x,y,2me,temperature,money

•  Ordinal–  Wecanputthevaluesinorder,butwecannotsay

thatonevalueisN2meslargerthansomeothervalue–  Example:levelofeduca2on(highschooldiploma,bachelor’sdegree,

master’sdegree,…)

•  Categorical(ornominal)–  Thereisnonaturalordering(exceptmaybealphabe2cal,

whichisarbitraryandlanguage-dependent)–  Example:foodgroups(meat,dairy,fruitsandvegetables,cereals)–  Example:bachelor’sinmechanicalengineering,bachelor’sincivil

engineering,etc.–  Example:Honda,Toyota,GM,Chrysler,etc.–  Example:countriesoftheworld

Output graphical representation: at most 3 spatial dimensions (often just 2), at most 1 temporal dimension (animation) … and also many graphical variables

Visualiza2onisamapping

Input data: each variable can be {independent, dependent} (i.e., a dimension or measure) and {quantitative, ordinal, categorical}

Hierarchyofgraphicalvariables(Mackinlay,1986)

Comparison of positions (common origin) in a barchart:

Comparison of lengths (different origins) in a stacked barchart:

Comparison of positions (common origin) in a grouped barchart:

Note: stacked barcharts are better than grouped barcharts for “part-to-whole” comparisons, even though this involves a length comparison, because the totals are not even shown in a grouped barchart.

Comparison of angles (common origin, and different origins):

Comparison of "densities" (color value) :

Comparison of color hue :

Comparison of areas :

scale

scale

Hierarchyofgraphicalvariables(Mackinlay,1986)

Astudytoconfirmthehierarchy(JeffreyHeeretMichaelBostock,"CrowdsourcingGraphicalPercep2on:Using

MechanicalTurktoAssessVisualiza2onDesign",CHI2010)

Positions

Lengths

Angles

Circular Areas

Rectangular areas

(aligned, or in a treemap)

Tableau

Quan2ta2vevariableasafunc2onofacategoricalvariable

Barchart

Quan2ta2vevariableasafunc2onofaquan2ta2vevariable

Linegraph

Quan2ta2vevariableasafunc2onof(ordinal)2me

Twodependentquan2ta2vevariables

Sca\erplot

Categoricalvariableasafunc2onofaquan2ta2vevariable

Gan\chart

Categoricalindependentvariable+quan2ta2veindependentvariable

Twoindependentcategoricalvariables

Crosstabula2on(“crosstab”)

Tableau applies heuristics like these to choose graphics according to the type of data.

Barchartversuslinegraph

Which makes it easier to see changes in slope ?

Tufte (1983)

Length vs area

IEEE Canadian Review, 2009, No. 60, page 31

ExamplesfromacoursebyMarilynOstergrenatUWashington

(h\p://courses.washington.edu/info424/Week3Prac2ce_ExcelGraphs.html)

http://www.research.ibm.com/people/l/lloydt/color/color.HTM Rogowitz and Treinish, “Why Should Engineers and Scientists Be Worried About Color?”

Borland and Taylor, “Rainbow Color Map (Still) Considered Harmful”, IEEE CG&A, 27(2):14-17, 2007

Classexercise:Designoneormoregraphicstovisualizeadatasetwiththefollowingvariables:

•  Carmodel:{Accord,AMCPacer,Audi5000,BMW320i,Champ,ChevNova,…}(19modelsintotal,onemodelforeachtuple;i.e.19tuples)

•  Carprice:[$0,$13500]•  Carmileage:[0,40]•  Repairrecord:{Great,Good,OK,Bad,Terrible}•  Carweight:[0,5500]

Most important variables

•  Carmodel:{Accord,AMCPacer,Audi5000,BMW320i,Champ,ChevNova,…}(19modelsintotal,onemodelforeachtuple;i.e.19tuples)

•  Carprice:[$0,$13500]•  Carmileage:[0,40]•  Repairrecord:{Great,Good,OK,Bad,Terrible}

•  Carweight:[0,5500]

Most important variables

mdmv data Marks of students taking 4 courses: •  Physics: 90% •  Math: 95% •  French literature: 65% •  History: 70%

Each student is like a tuple: •  (90%, 95%, 65%, 70%) •  Etc.

Parallel Coordinates (Alfred Inselberg)

100%

0%

Physics Math French Literature History

(90%, 95%, 65%, 70%)

Parallel Coordinates (Alfred Inselberg)

100%

0%

Physics Math French Literature History

(90%, 95%, 65%, 70%)

(30%, 20%, 90%, 90%)

Scatterplot Matrix (SPLOM)

Physics

Math

French Literature

History

(90%, 95%, 65%, 70%)

French Literature Math

Scatterplot Matrix (SPLOM)

Physics

Math

French Literature

History

(90%, 95%, 65%, 70%)

(30%, 20%, 90%, 90%)

French Literature Math

Sca\erplotMatrixorSPLOM

Nik

las

Elm

qvis

t, P

ierr

e D

ragi

cevi

c, J

ean-

Dan

iel F

eket

e (2

008)

. “R

ollin

g th

e D

ice:

Mul

tidim

ensi

onal

Vis

ual E

xplo

ratio

n us

ing

Sca

tterp

lot M

atrix

Nav

igat

ion”

. P

roce

edin

gs o

f Inf

oVis

200

8.

Within each scatterplot, we could be interested in seeing outliers, correlations, etc.

Notice: the upper triangular half is the same as the lower triangular half, and the diagonal is not very interesting.

Sca\erplotMatrixorSPLOM

Wilkinson, Anand, Grossman, “Graph-Theoretic Scagnostics”, 2005

Note: the diagonal is used to show the names of the variables

Matrixofcorrela2oncoefficientsWhenwehavemanymeasures,wecansummarizeeachsca\erplotbycompu2ngitscorrela2oncoefficientanddisplayingonlythat,insteadof

displayingalltheindividualdatapoints.Thebelowinterfacealsoallowstheusertoselectonesca\erplotandseeazoomed-inviewfordetails.

Jinwook Seo and Ben Shneiderman, “A Rank-by-Feature Framework for …”, Proceedings of InfoVis 2004. Implemented in HCE ( http://www.cs.umd.edu/hcil/hce/ )

Sca\erDice(Elmqvistetal.2008)h\ps://www.youtube.com/watch?v=2bYIRcO-gwg

ExamplefromMatlab:“carbig.mat”

http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/mvplotdemo.html

Summaryoftechniquesforvisualizingmdmvdata

•  1dimension+1measure:barchart,linechart

•  0dimensions+2measures:sca\erplot

•  2dimensions+1measure:parallelbarcharts,heatmap

•  Upto≈6dimensions+≈4measures:dimensionalstacking

•  Upto≈2dimensions+≈20measures:glyphs,parallelcoordinates,sca\erplotmatrix

•  Howcanwevisualizemanydimensions?

?

“NutsandBolts”dataset(72rows):

Region Month Product Sales Equipment_costs Labor_costs

0 0 0 2.76 0.92 4.30 0 1 4.92 1.64 4.30 1 0 4.2 1 4.30 1 1 8.4 2 4.30 2 0 5.28 9.6 4.30 2 1 14.52 26.4 4.30 3 0 5.016 0.88 4.30 3 1 8.436 1.48 4.3… … … … … …2 10 0 8.82 2.1 4.92 10 1 9.156 2.18 4.92 11 0 5.655 1.45 5.22 11 1 9.4965 2.435 5.2

Dimensions Measures

“NutsandBolts”dataset

“NutsandBolts”dataset

Not very useful

The SPLOM works well with mesures, but not with dimensions

“NutsandBolts”dataset

“NutsandBolts”dataset

Not very useful

Parallel coordinates work well with mesures, but not with dimensions

“NutsandBolts”dataset

Each of the above examples only show 4 of the 6 variables. Showing all 6 variables (3 dimensions and 3 mesures) would require much space.

Example view that would be possible with Tableau (dimensional stacking):

“NutsandBolts”datasetExample view that would be possible with Tableau (dimensional stacking):

The above example only shows 4 of the 6 variables. One of these is “Month”, which has 12 levels, greatly increasing space requirements.

Glyphs

dimension

dimension

measure

dimension

measure

measure

Glyphs can show many measures at once, but cannot easily show more than 2 dimensions at once.

GeneralizedPLOtMatrix(GPLOM)ofthe“NutsandBolts”dataset

Scales better than Tableau’s dimensional stacking to a large number of dimensions (and can also show many measures)

GeneralizedPLOtMatrix(GPLOM)[Im,McGuffin,Leung,IEEEInfoVis2013]

Summaryoftechniquesforvisualizingmdmvdata

•  1dimension+1measure:barchart,linechart

•  0dimensions+2measures:sca\erplot

•  2dimensions+1measure:parallelbarcharts,heatmap

•  Upto≈6dimensions+≈4measures:dimensionalstacking

•  Upto≈2dimensions+≈20measures:glyphs,parallelcoordinates,sca\erplotmatrix

•  Upto≈12dimensions+≈12measures:generalizedplotmatrix