What is Data visualization with examples

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Chun-houhChen WolfgangHärdle AntonyUnwin Editors Handbookof DataVisualization WithFiguresandTables 1234 AntonyUnwin,Chun-houhChen,WolfgangK.Härdle ComputationalStatistics 1.1 andDataVisualization hisbookisthethirdvolumeoftheHandbookofComputationailcSstaantdisctov- ersthe field of data visualization. Inline with the companion volumes, it contains acollectionofchaptersbyexpertsinthefieldtopresentreaderswithanup-to-date andcomprehensiveoverviewofthestateoftheart.Datavisunailsizaantaioctivearea ofapplicationandresearch,andthisisagoodtimetogathertogetherasummaryof currentknowledge. Graphicdisplaysareotenveryeffectiveatcommunicatinginformation.heyare alsoveryotennoteffectiveatcommunicating information.Twoimptor antreasons for this state of affairs are that graphics can be produced with clicaksfeofwthe mousewithoutanythoughtandthedesignofgraphicsisnottakenserinoyuslyinma scientifictextbooks.Somepeopleseemtothinkthatpreparinggoodgraphicsisjust a matter of common sense (inwhichcase their common sense cannot be in good shape),whileothersbelievethatpreparinggraphicsisalow-leveltask,notappropri- ateforscientificattention.hisvolumeoftheHandbookofComputlatStion ataistics takesgraphicsfordatavisualizationseriously. 1.1.1 DataVisualizationandTheory Graphicsprovideanexcellentapproachforexploringdataandareessentialforpre- sentingresults.Althoughgraphicshavebeenusedextensivelyinstatisticsforalong time,thereisnotasubstantive bodyoftheoryaboutthetopic.Quitealotofatten- tionhasbeenpaidtographicsforpresentation,particularlysincethesuperbbooksof EdwardTute.However,thisknowledgeisexpressedinprinciplestobefollowedand notinformaltheories. Bertin’sworkfromthesisotencbiut tedhasnotbeen developedfurther.hisisacuriousstateofaffairs.Graphicsareusedagreatdealin manydifferentfields,andonemightexpectmoreprogresstohavebeenmadealong theoreticallines. Sometimesinsciencethetheoreticalliteratureforasubjectisconsiderablewhile thereislittleappliedliteraturetobefound.heliteratureondatavisualizatioynisver muchtheopposite.Examplesaboundinalmosteveryissueofeveryscientificjour- nalconcernedwithquantitativeanalysis.hereareoccasionallyarticlespublishedin amoretheoreticalveinaboutspecificgraphicalforms,butlittlelt elsh e.oAughthere isarespected statistics journal called the Journal of Computational and Graphical Statistics,mostofthepaperssubmittedthereareincomputationalstatistics.Perhaps this isbecause it iseasier topublish astudy ofatechnical computational problem thanitistopublishworkonimprovingagraphicdisplay. 1.1.2 PresentationandExploratoryGraphics he differences between graphics for presentation and graphircsexfoploration lie in both form and practice. Presentation graphics are generally static, and a singleIntroduction 5 Figure..Abarchartofthenumberofauthorsperpaper,ahistogramofthenpuamgebserpeorf paper,andparallelboxplotsoflengthbynumberofauthors.Paperswi moth rethanthreeauthorshave beenselected graphicisdrawntosummarizetheinformationtobepresented.hesedisplaysshould beofhighqualityandincludecompletedefinitionsandexplanatiotnshofevariables shownandoftheformofthegraphic.Presentationgrapheicpsrar oof elsikofmath- ematical theorems; they maygive nohint astohowaresult wasreached, but they shouldofferconvincingsupportforitsconclusion.Exploratorygracpsh ,oni theother hand, are used for looking for results. Very many of them may be used, and they shouldbefastandinformative rather thanslowandprecise.heyarinetneot nded forpresentation,sothatdetailedlegendsandcaptionsareunnecessary.Onepresen- tation graphic will bedrawnforviewing bypotentially thousands ofreaderswhile thousandsofexploratorygraphicsmaybedrawntosupportthedatainvestigations ofoneanalyst. Booksonvisualizationshouldmakeuseofgraphics.Figure.showssomesimple summaries of data about the chapters in this volume, revealing that over half the chapters had more than one author and that more authors does not always mean longerpapers. GraphicsandComputing 1.1.3 Developmentsincomputingpowerhavebeenofgreatbenefittographicsinrecent years.Ithasbecomepossibletodrawprecise,complexdisplayswithgreateaseand to print them with impressive quality at high resolution. hat was not always the case, and initially computers were more a disadvantage for graphics. Computing screensandprinterscouldatbestproduceclumsyline-drivendisplaysoflowresolu- tionwithoutcolour.heseofferednocompetition tocareful,hand-ddrisaw plnays. Furthermore,evenearlycomputersmademanycalculationsmucheasierthanbefore andallowedfittingofmorecomplicatedmodels.hisdirectedattention awayfrom graphics, and itisonly inthe lastyears that graphics have come intotheir own again.6 AntonyUnwin,Chun-houhChen,WolfgangK.Härdle hese comments relate to presentation graphics, that is, graphics drawnfor the purposeofillustrating andexplainingresults.Computingadvanceshavebenefitted exploratory graphics, that is, graphics drawn to support exploring data, far more. Notjustthequalityofgraphicrepresentationhasimprovedbutalsotheqisuantity.It nowtrivialtodrawmanydifferentdisplaysofthesamedataortoriffleth hrma oungy differentversionsinteractivelytolookforinformationindata.hesecapabiliaties re onlygraduallybecomingappreciatedandcapitalizedon. heimportanceofsotwareavailabilityandpopularityindeterminingwhatanal- ysesarecarriedoutandhowtheyarepresentedwillbeaninterestingresearchtopic forfuturehistoriansofscience.Inthebusinessworld,noones mseetobeableto dowithoutthespreadsheetExcel.IfExceldoesnotofferaparticular graphicform, then that form will not be used. (In fact Excel offers many graphic forms, though notallthatastatistician wouldwant.)Manyscientists, whoonlyrarelyneedaccess tocomputational power,alsorelyonExcelanditsoptions.Inthewoforsltdatistics itself,thepackagesSASandSPSSwerelongdominant.Inthelastyears,firstSand S-plusandnowRhaveemergedasimportant competitors.Noneofth paecskeages currentlyprovideeffectiveinteractivetoolsforexploratorygraphics,thoughtheyare allmovingslowlyinthatdirectionaswellasextendingtherangeandflexibilityofthe presentationgraphicstheyoffer. Datavisualization isanewterm.Itexpressestheideathatitinvolves morethan justrepresentingdatainagraphicalform(insteadofusingatable).heinformation behind the data should also be revealed in a good display; the graphic should aid readersorviewersinseeingthestructureinthedata.hetermdatavisualizationis related tothe new field of information visualization. hisincludes visualization of allkindsofinformation, notjustofdata, andiscloselyassociated withresearchby computerscientists.Uptillnowtheworkinthisareahastendedtoconcentratejust onpresentinginformation,ratherthanonwhatmaybededucedfromit.Statisticians tendtobeconcernedmorewithvariabilityandtoemphasizethestatisticalproperties ofresults.hecloserlinkingofgraphicswithstatisticalmodellingcanmakmeotre his explicitandisapromisingresearchdirectionthatisfacilitatedbytheflexiblenature ofcurrentcomputingsotware.Statisticianshaveanimportantroletoplayhere. 1.2 TheChapters Needlesstosay,eachHandbookchapterusesalotofgraphicdisplays.Figure.is ascatterplot ofthe number offiguresagainstthe number ofpages.hereisanap- proximatelinearrelationshipwithacoupleofpapershavingsomewhatmorefigures perpageandonesomewhatless.hescaleshavebeenchosentomaximizethedata- inkratio.Analternative versionwithequalscalesmakesclearerthatthenumberof figuresperpageisalmostalwayslessthanone. he Handbook has been divided into three sections: Principles, Methodology, andApplications.Needlesstosay,thesectionsoverlap.Figure.isabinarymatrix visualization using Jaccard coefficients for both chapters (rows) and index entriesIntroduction 7 Figure..Ascatterplotofthenumberoffiguresagainstthenumberofpagesforthe dbooHk’asn chapters (columns)toexplorelinksbetweenchapters.Intherawdatamap(lower-letportion of Fig. .)there isa banding ofblack dots from the lower-lettoupper-rightcor- nersindicatingapossibletransitionofchapter/indexcombinations.Intheproximity mapofindices(upperportionofFig..),indexgroupsA,B,C,D,andEareover- lappedwitheachother andare dominated bychaptersofGoodGraphics, History, FunctionalData,MatrixVisualization,andRegressionbyPartsrespectively. SummaryandOverview;PartII 1.2.1 hetenchaptersinPartIIareconcernedwithprinciplesofdatavisualization. First there is an historical overview by Michael Friendly, the custodian of the Internet GalleryofDataVisualization,outliningthedevelopmentsingraphicaldisplaysover thelastfewhundredyearsandincludingmanyfineexamples. InthenextchapterAntonyUnwindiscussessomeoftheguidelinesfortheprepa- rationofsoundandattractive datagraphics.hequestionmarkinthechaptertitle sumsitupwell:whatever principlesorrecommendations arefollowed,thesuccess ofagraphicisamatteroftaste;therearenofixedrules. heimportanceofsotwareforproducinggraphicsisincontroverti.blPaeulMur- rell in his chapter summarizes the requirements for producing accurate and exact staticgraphics.Heemphasizesboththeneedforflexibilityincustomizingstandard plotsandtheneedfortoolsthatpermitthedrawingofnewplottypes. Structureindatamayberepresentedbymathematicalgraphs.GeorgeMichailidis pursuesthisideainhischapterandshowshowthisleadstoanotherclassofgraphic displaysassociatedwithmultivariateanalysismethods.8 AntonyUnwin,Chun-houhChen,WolfgangK.Härdle Figure..MatrixvisualizationsoftheHandbookwithchaptersintherow desxanendtirniesinthe columns Lee Wilkinson approaches graph-theoretic visualizations from another point of view,andhisdisplaysareconcernedpredominantly,thoughbynomeansexclusively, withtrees,directedgraphsandgeometricgraphs.Healsocovelarsyotuh toefgraphs, atrickyproblemforlargenumbersofvertices,andraisestheintriguingissueofph gra matching. Mostdatadisplaysconcentrateononeortwodimensions.hisisfrequentlysuffi- cienttorevealstrikinginformationaboutadataset.Togaininsightintomultivariate structure,higher-dimensionalrepresentations arerequired.Martinheusdiscusses themainstatisticalgraphicsofthiskindthatdonotinvolvedimensionreductionand comparestheirpossiblerangeofapplication. Everyone knowsaboutChernofffaces,thoughnotmanyeverusethem.hepo- tentialofdataglyphsforrepresentingcasesininformativeandproductivyesh waas notbeenfullyrealized.MattWardgivesanoverviewofthewidevarietyofpossible formsandofthedifferentwaystheycanbeutilized.Introduction 9 here are two chapterson linking. Adalbert Wilhelm describes a formal model forlinkedgraphicsandtheconceptualstructureunderlyingit.Heisabletoencom- passdifferenttypesoflinking anddifferentrepresentations. Graham Willslooksat linkinginamoreappliedcontextandstressestheimportanceofdistinguishingbe- tweenviewsofindividualcasesandaggregatedviews.Healsohighlightsthevariety ofselectionpossibilitiesthereareininteractivegraphics.Bothchapterspointoutthe valueoflinkingsimpledataviewsoverlinkingcomplicatedones. hefinalchapterinthissectionisbySimonUrbanek.Hedescribesthegraphics thathavebeenintroducedtosupporttreemodelsinstatistics.hecloseassociation betweengraphicsandthemodels(andcollectionsofmodelsinforests)isparticularly interestingandhasrelevanceforbuildingcloserlinksbetweengraphicsandmodels inotherfields. SummaryandOverview;PartIII 1.2.2 hemiddleandlargestsectionoftheHandbookconcentrates oniviinddualareaof graphicsresearch. Geographicaldatacanobviouslybenefitfromvisualization.MuchofBertin’swork wasdirectedatthiskindofdata.JuergenSymanzikandDanielCarrwriteaboutmi- cromaps (multiple small images of the same area displaying different parts of the data)andtheirinteractiveextension. Projectionpursuitandthegrandtourarewellknownbutnoteasytouse.Despite theavailabilityofattractivefreesotware,itisstilladifficulttasktoda anal tasyseetsin depthwiththisapproach.DianneCook,AndreasBuja,Eun-KyungLeeandHadley Wickhamdescribetheissuesinvolvedandoutlinesomeoftheprogressthathasbeen made. Multidimensionalscalinghasbeenaroundforalongtime.MichaelCoxandTrevor Cox(norelation,butanMDSwoulddoubtlessplacethemclosetogether)reviewthe currentstateofresearch. Advancesinhigh-throughputtechniq nindues ustr i ialprojects,academicstudies andbiomedicalexperimentsandtheincreasingpowerofcomputersfordatacollec- tionhaveinevitablychangedthepracticeofmoderndataanalysis.Real-lifedatasets become larger and larger in both sample size and numbers of variabls.eFrancesco Palumbo,AlainMorineauandDomenicoVistoccoillustrateprinciplesofvisualiza- tionforsuchsituations. Someareasofstatisticsbenefitmoredirectlyfromvisualizationthanothers.Den- sityestimationishardtoimaginewithoutvisualization.MichaelMinnotte,SteveSain andDavidScottexamineestimationmethodsinuptothreedimensions.Inter yestingl therehasnotbeenmuchprogresswithdensityestimationineventhreedimensions. Sets of graphs can be particularly useful for revealing the sturreucitn datasets andcomplementmodellingefforts.RichardHeibergerandBurtHollanddescribean approachprimarilymakinguseofCartesianproductsandtheTrellisparadigm.Wei- YinLohdescribestheuseofvisualizationtosupporttheuseofregressionmodels,in particularwiththeuseofregressiontrees.10 AntonyUnwin,Chun-houhChen,WolfgangK.Härdle Insteadofvisualizing thestructureofsamplesorvariablesinagivendataset,re- searchersmaybeinterestedinvisualizingimagescollectedwithcertainformats.Usu- allythetargetimagesarecollectedwithvarioustypesofnoisepatternanditisneces- sarytoapplystatistical ormathematical modellingtoremoveordiminishthenoise structurebeforethepossiblegenuineimagescanbevisualizJeödr.gPolzehlandVlad- imirSpokoinypresentonesuchnoveladaptivesmoothingprocedureinreconstruct- ingnoisyimagesforbettervisualization. he continuing increase in computer powerhashad many different impacts on statistics.Computationallyintensivesmoothingmethodsarenowcommonplace,al- thoughtheywereimpossibleonlyafewyearsago.AdrianBowmangivesarnvoievwe oftherelationsbetweensmoothingandvisualization.Yuan-chinChang,Yuh-JyeLee, Hsing-KuoPao,Mei-HsienLeeandSu-YunHuanginvestigate theimpactofkernel machinemethodsonanumberofclassicaltechniques:principalcomponents,canon- icalcorrelationandclusteranalysis.heyusevisualizationstocomparetheirresults withthosefromtheoriginalmethods. Clusteranalyseshaveotenbeenabitsuspecttostatisticians. helackofformal modelsinthe pastand the difficulty ofjudging the successofthe clusteringswere bothnegative factors.FritzLeischconsidersthegraphical evaluation ofclusterings andsomeofthepossibilitiesforasoundermethodologicaloaapcph r . Multivariatecategoricaldataweredifficulttovisualizeinthepast.hechapterby David Meyer, Achim Zeileis and Kurt Hornik describes fairly classical approaches forlowdimensionsandemphasizesthelinktomodelbuilding.HeikeHofmannde- scribesthe powerful toolsofinteractive mosaicplots that have become ainvailable recent years, not least through her own efforts, and discusses how different varia- tionsoftheplotformcanbeusedforgaininginsightintomultivariatedatafeatures. AlfredInselberg,theoriginalproposerofparallelcoordinateplots,offersaner- ov viewofthisapproachtomultivariatedatainhisusualdistinctivestyle.Herehecon- sidersinparticularclassificationproblemsandhowparallelcoordinateviewscanbe adaptedandamendedtosupportthiskindofanalysis. Most analyses using graphics make use of a standard set of graphical tools, for example,scatterplots,barcharts,andhistograms.Han-Min,gSh WuengLiTzengand Chun-houhChendescribeadifferentapproach,builtarouncdoluou sinrgapproxi- mationsforindividualvaluesinadatamatrixandapplyingcluesrtanalysestoorder thematrixrowsandcolumnsininformativeways. FormanyyearsBayesianswereprimarilytheoreticians. hankstoMCMCmeth- ods they are now able to also apply their ideas to great effect. his has led to new demands in assessing model fit and the quality of the results. Jouni Kerman, An- drewGelman,TianZhengandYuejingDingdiscussgraphicalapprcoh a esfortack- lingtheseissuesinaBayesianframework. Withoutsotwaretodrawthedisplays,graphicanalyisisalmostimpossiblenowa- days.JunjiNakano,YamamotoYoshikazuandKeisukeHondaareworkinognJava- basedsotwaretoprovidesupportfornewdevelopments,andtheyoutlinetheirap- proachhere.ManyresearchersareinterestedinprovidingtoolsviatheWeb.Yoshiro Yamamoto,MasayaIizukaandTomokazuFujinodiscussusingXMLforinteractive statisticalgraphicsandexplaintheissuesinvolved.Introduction 11 SummaryandOverview;PartIV 1.2.3 hefinal section contains sevenchaptersonspecificapplications ofdatavisualiza- tion. hereare,ofcourse,individual applications discussedinearlier chapters,but heretheemphasisisontheapplicationratherthanprinciplesormethodology. Geneticnetworksareobviouslyapromisingareaforinformativegraphicdisplays. GraceShiehandChin-YuanGuodescribesomeoftheprogressmoafdareasndmake clearthepotentialforfurtherresearch. Modern medical imaging systems have made significant contributions to diag- noses and treatments. Henry Lu discusses the visualization of data from positron emissiontomography,ultrasoundandmagneticresonance. Twochaptersexaminecompanybankruptcydatasets.Inthefirstone,AntonyUn- win,MartinheusandWolfgangHärdleuseabroadrangeofvisualization toolsto carry out an extensive exploratory data analysis. No large datasean t cbe analysed cold,andthischaptershowshoweffectivedatavisualizationcanbeinassessingdata quality and revealing features of a dataset. he other bankruptcy chapter employs graphicstovisualizeSVMmodelling.WolfgangHärdle,RouslanMor oandDorothea Schäferusegraphicstodisplayresultsthatcannotbepresentedinaclosedanalytic form. heastonishing growthofeBayhasbeenoneofthebigsuccessstoriesofrecent years.WolfgangJank,GalitShmueli,CatherinePlaisantandBenShneidermanhave studieddatafromeBayauctionsanddescribetherolegraphicsplayedintheiranal- yses. KrzysztofBurneckiandRafalWeronconsidertheapplication ofvisualization in insurance. his is another example of how the value of graphics lies in providing insightintotheoutputofcomplexmodels. TheAuthors 1.2.4 heeditorswouldliketothanktheauthorsofthechaptersfortheircontributions.It isimportantforacollective workofthiskindtocoverabroadrange andtogather manyexpertswithdifferentintereststogether.Wehavebeenfortunateinreceiving theassistanceofsomanyexcellentcontributors. hemixtureattheendremains,ofcourse,amixture.Differentauthorstakedif- ferent approachesand have different styles. It early became apparent that even the termdatavisualizationmeansdifferentthingstodifferentpeopleWehopethatthe Handbookgainsratherthanlosesbythiseclecticism. Figures.and.earlierinthechaptershowedthatthechapterformvariedbe- tweenauthorsinvariousways.Figure.revealsanotheraspect.hescatterplotshows anoutlier withavery large number ofreferences(the historical survey ofMichael Friendly)andthatsomepapersreferencedtheworkoftheirownauthorsmorethan others.hehistogramisfortherateofself-referencing.12 AntonyUnwin,Chun-houhChen,WolfgangK.Härdle Figure..Ascatterplotofthenumberofreferencestopapersbyachapter’sautho instrsthe aga total numberofreferencesandahistogramoftherateofself-referencing 1.3 Outlook here are many open issues in data visualization and many challenging research problems.hedatasetstobeanalysedtendtobemorecomplexandacreertainly becoming larger all the time. he potential of graphical tools for exploratory data analysishasnotbeenfullyrealized,andthecomplementaryinterplaybetweenstatis- ticalmodellingandgraphicshasnotyetbeenfullyexploited.Advancesincomputer sotwareandhardwarehavemadeproducinggraphicseasier,buttheyhavealsocon- tributedtoraisingthestandardsexpected. Futuredevelopments will undoubtedly includemoreflexible andpowerfulsot- wareandbetterintegration ofmodellingandgraphics.herewrilolbpablybeindi- vidual newandinnovative graphicsand someimprovements inthegeneral design of displays. Gradual gains in knowledge about the perception ofpgh raics and the psychologicalaspectsofvisualization willleadtoimprovedeffectiveness ofgraphic displays.Ideallythereshouldbeprogressintheformaltheoryofdatavisualization, butthatisperhapsthebiggestchallengeofall.PartII PrinciplesABriefHistory II.1 ofDataVisualization MichaelFriendly 1.1 Introduction........................................................................................ 16 1.2 MilestonesTour................................................................................... 17 Pre-17thCentury:EarlyMapsandDiagrams............................................. 17 1600–1699: Measurement andTheory..................................................... 19 1700–1799: NewGraphicForms.............................................................. 22 1800–1850: Beginnings ofModernGraphics ............................................ 25 1850–1900: TheGoldenAgeofStatisticalGraph...ics ................................ 28 1900–1950: TheModernDarkAges ......................................................... 37 1950–1975: RebirthofDataVisualizat...i.... on.......................................... 39 1975–present: High-D,InteractiveandDynamicDataVisuali.... zat... i.... on 40 1.3 StatisticalHistoriograph...... y ............................................................ 42 Historyas‘Data..’.................................................................................... 42 AnalysingMilestonesDa... ta................................................................... 43 WhatWasHeThinking? –Understanding ThroughReproduc.t..i.... on....... 45 1.4 FinalThoughts.................................................................................... 4816 MichaelFriendly Itiscommontothinkofstatisticalgraphicsanddatavisualizationasrelativelymod- erndevelopmentsinstatistics.Infact,thegraphicrepresentationofquanin- titative formationhasdeeproots.heserootsreachintothehistoriesoftheearliestmapmak- ingandvisualdepiction,andlaterintothematiccartography,statisticsandstatistical graphics, medicine and other fields. Along the way, developments in technologies (printing,reproduction),mathematicaltheoryandpractice,andempiricalobserva- tionandrecordingenabledthewideruseofgraphicsandnewadvancnesfoirmand content. his chapter provides an overview of the intellectual history of data visualiza- tionfrommedievaltomoderntimes,describingandillustratingsomesignificantad- vancesalongtheway.Itisbasedonaproject,calledt Mh ileestones Project,tocollect, catalogueanddocumentinoneplacetheimportantdevelopmentsinawiderangeof areasandfieldsthatledtomoderndatavisualization.hisefforthassuggestedsome questionsconcerningtheuseofpresent-daymethodsofanalysinguan ndderstand- ingthishistory,whichIdiscussundertherubricof‘statisticalhistoriography.’ 1.1 Introduction he only new thing in the world is the history you don’t know –H .arrySTruman Itiscommontothinkofstatisticalgraphicsanddatavisualizationasrelativelymod- erndevelopmentsinstatistics.Infact,thegraphicportrayalofquantitativeinforma- tionhasdeeproots.heserootsreachintothehistoriesoftheearliestmap-making and visual depiction, and later into thematic cartography, statistics and statistical graphics,withapplications andinnovations inmanyfieldsofmedicineandscience whichareotenintertwinedwitheachother.heyalsoconnectwiththeriseofstatis- ticalthinkingandwidespreaddatacollectionforplanningandcommerceupthrough thethcentury.Alongtheway,avarietyofadvancementscontributedtothewide- spreaduseofdata visualization today.heseincludetechnologies fordrawing and reproducingimages,advancesinmathematicsandstatistics,andnewdevelopments indatacollection,empiricalobservationandrecording. Fromaboveground,wecanseethecurrentfruitandanticipatefuturegroweth;w mustlookbelowtounderstandtheirgermination.Yetthegreatvarietyofrootsand nutrientsacrossthesedomains,whichgaverisetothemanybranchesweseetoday, are oten not well known and have never been assembled in a single garden to be studiedoradmired. his chapter provides an overview of the intellectual history of data visualiza- tion from medieval to modern times, describing and illustrating some significant advancesalongtheway.ItisbasedonwhatIcalltheMilestonesProject,anattempt toprovide abroadly comprehensive and representative catalogue ofimportae-nt d velopmentsinallfieldsrelatedtothehistoryofdatavisualization.ABriefHistoryofDataVisualization 17 here are many historical accounts of developments within the fields of proba- bility (Hald, ),statistics (Pearson, ; Porter, ; Stigler,),astronomy (Riddell,) and cartography (Wallisand Robinson, ),whichrelate intto er, alia, some of the important developments contributing to modern data visualiza- tion. here are other, more specialized, accounts which focus on the early history ofgraphicrecording(HoffandGeddes,,),statisticalpghs ra (Funkhouser, , ; Royston, ; Tilling, ), fitting equations to em ripcail data (Fare- brother, ),economics and time-series graphs (Klein,),cartography (Friis, ; Kruskal, ) and thematic mapping (Robinson, ; Palys,k) and so forth; Robinson (Robinson, , Chap. ) presents an excellent overview ofesom oftheimportantscientific,intellectualandtechnicaldevelopmentsoftheth–th centuriesleadingtothematiccartographyandstatisticalthinking.WainerandVelle- man()providearecentaccountofsomeofthehistoryofstatisticalgraphics. Buttherearenoaccounts whichspantheentire developmentofvisual thinking andthevisualrepresentationofdataandwhichcollatethecontributionsofdisparate disciplines.Inasmuchastheirhistoriesareintertwined,sotooshouldbeanytelling ofthedevelopmentofdatavisualization. Anotherreasonfor rwienatveingtheseac- counts is that practitioners in these fields today tend to be highly specialized and unaware ofrelated developments inareas outside their domain, muchlessoftheir history. MilestonesTour 1.2 Every picture tells a story. –RodStewart, Inorganizingthishistory,itprovedusefultodividehistoryicnt hose,peaochofwhich turnedouttobedescribablebycoherentthemesandlabels.hisdivisionis,ofcourse, somewhatartificial,butitprovidestheopportunitytocharacterizetheaccomplish- mentsineachperiodinageneralwaybeforedescribingsomeoftheminmoredetail. Figure., discussed inSect. ..,providesagraphic overview ofthe epochsIde- scribe in the subsections below, showing the frequency of events considered mile- stonesintheperiodsofthishistory.Fornow,itsufficestonaot beelstah ttealchedto theseepochs,asteadyrisefromtheearlythcenturytothelateth thcentury,wi acuriouswigglethereater. Inthelargerpicture–recounting the historyofdatavisualization –itturnsout that many of the milestone items have astory tobe told: What motivated this de- velopment? What wasthe communication goal? Howdoes it roelat otehter devel- opments–Whatwerethe precursors?Howhasthisideabeenusedorre-invented today?Eachsectionbelowtriestoillustratethegeneralthemeswithafewexemplars. Inparticular,thisaccountattemptstotellafewrepresentativestoriesofitoh ds,eseper ratherthantotrytobecomprehensive. Forreasonsofeconomy,onlyalimitednumberofimagescouldbeprintedhere, andtheseonlyinblackandwhite.OthersarereferredtobyWeblinks,mostlyfrom18 MichaelFriendly Figure..Timedistributionofeventsconsideredmilestonesinthehistoryofda uatliza avis tion,shown byarugplotanddensityestimate the Milestones Project, http://www.math.yorku.ca/SCS/Gallery/milestone/, where acolourversionofthischapterwillalsobefound. 1.2.1 Pre-17thCentury:EarlyMapsandDiagrams heearliestseedsofvisualizationaroseingeometricdiagrams,intablesoftheposi- tionsofstarsandothercelestialbodies,andinthemakingoftmoaaipds innavigation andexploration.heideaofcoordinateswasusedbyancientEgyptiansurveyorsin layingouttowns,earthlyandheavenlypositionswerelocatedbysomeatkh ining to latitudeandlongitudebyatleastB.C.,andthemapprojectionph ofaersicalearth intolatitudeandlongitudebyClaudiusPtolemyc.–c.inAlexandriawldou serveasreferencestandardsuntilthethcentury. Amongtheearliestgraphicaldepictionsofquantitative inifon ormisatananony- mousth-centurymultipletime-seriesgraphofthechangingpositionoftheseven mostprominentheavenlybodiesoverspaceandtime(Fig..),describedbyFunk- houser()andreproducedinTute(,p.).heverticalaxisrepresentsthe inclination of the planetary orbits; the horizontal axis shows time, divided into  intervals. hesinusoidal variation withdifferentperiodsisnotable, asistheuseof agrid,suggestingbothanimplicitnotionofacoordinatesystemandsomethingakin tographpaper,ideasthatwouldnotbefullydevelopeduntilth –es. Inthethcentury,theideaofplottingatheoreticalfunction(asaprpoh) tobargra and the logical relation between tabulating values and plotting them appeared inABriefHistoryofDataVisualization 19 Figure..Planetarymovementsshownascyclicinclinationsovertime,byanknuonwnastronomer, appearinginath-centuryappendixtocommentariesbyA.T.MabciurosonCicero’s In Somnium Sciponis. Source:Funkhouser(,p.)  a work by Nicole Oresme –Bishop of Liseus(Oresme, , ), fol- lowedsomewhatlaterbytheideaofatheoreticalgraphofdistancevs.speedbyNico- lasofCusa. Bythethcentury,techniquesandinstrumentsforpreciseobservationandmea- surementofphysicalquantities andgeographic andcelestial positionwerewellde- veloped(forexample,a‘wallquadrant’constructedbyTychoBrahe–co, v- eringanentirewallinhisobservatory).Particularlyimportantwerethe elopdmen ev t oftriangulationandothermethodstodeterminemappinglocationsaccurately(Fri- sius,;Tartaglia,).Aswell,weseeinitialideasforcapturingimagesdirectly (thecamera obscura, used by Reginer Gemma-Frisius intorecord an eclipse ofthesun),therecordingofmathematical functionsintables(trigonometrictables byGeorg Rheticus, )and the firstmodern cartographiche atlas atr(um Orbis TerrarumbyAbrahamOrtelius,).heseearlystepscomprisethebeginningsof datavisualization. 1600–1699:MeasurementandTheory 1.2.2 Amongst the most important problems of the th century were those concerned withphysical measurement –oftime,distance and space–forastronomy, survey-  Funkhouser(,p.)wassufficientlyimpressedwithOresme’sgraspoftherelationbe- tweenfunctionsandgraphsthatheremarked,‘Ifapioneeringcontemporaryhadcollected somedataandpresentedOresmewithactualfigurestoworkupon,wemighthavehadsta- tisticalgraphsfourhundredyearsbeforePlayfair.’20 MichaelFriendly ing,mapmaking,navigation andterritorial expansion. hiscenturyalsosawgreat new growth in theory and the dawn of practical application – the rise of analytic geometryandcoordinatesystems(DescartesandFermat),theoriesoferrorsofmea- surementandestimation (initialstepsbyGalileointheanalysisofobservations on TychoBrahe’sstarof(Hald,,§.)),thebirthofprobah bieliotryyt(Pascal andFermat)andthebeginningsofdemographicstatistics(JohnGraunt)and‘politi- calarithmetic’(WilliamPetty)–thestudyofpopulation,land,taxes,valueofgoods, etc.forthepurposeofunderstandingthewealthofthestate. Earlyinthiscentury,ChristopherScheiner(–,recordingsfrom)in- troduced an idea Tute () would later call the principle of ‘small multiples’ to showthechangingconfigurationsofsunspotsovertime,shown.in.h Fige.m  ul- tipleimagesdepicttherecordingsofsunpotsfromOctoberuntilDecember ofthatyear.helargekeyintheupperletidentifiessevengroupsofsunspyothe tsb lettersA–G.hesegroupsaresimilarlyidentified inthesmaller images,arrayed lettorightandtoptobottombelow. Anothernoteworthyexample(Fig..)showsagraphicby aelMi Flcoh rent vanLangren–,aFlemishastronomertothecourtofSpain,believedtobe thefirstvisualrepresentationofstatisticaldata(Tute,,p.).Atthatotime, f lack Figure..Scheiner’srepresentationofthechangesinsunspotsoverSotiume. rce:Scheiner (–)ABriefHistoryofDataVisualization 21 Figure..Langren’sgraphofdeterminationsofthedistance,inlongitfruodme,ToledotoRome.  ′ hecorrectdistanceis . Source:Tute(,p.)  areliablemeanstodeterminelongitudeatseahinderednavigationandexploration. his-Dlinegraphshowsallknownestimatesofthedifferenceinlongitude be- tween Toledoand Romeandthe name ofthe astronomer (Mercator, TychoBrahe, Ptolemy,etc.)whoprovidedeachobservation. WhatisnotableisthatvanLangrencouldhavepresentedthisinformationinvar- ioustables–orderedbyauthortoshowprovenance,bydatetoshoroit wyp,ror i by distance.However,onlyagraphshowsthewidevariationintheestimates;notethat therangeofvaluescoversnearlyhalfthelengthofthescale.VanLangrentookashis overallsummarythecentreoftherange,wheretherehappenedtobealargeenough gapforhimtoinscribe‘ROMA.’Unfortunately,alloftheestimateswerebiasedup-  ′ wards;thetruedistance( )isshownbythearrow.VanLangren’sgraphisalso amilestoneastheearliestknownexemplaroftheprincipleof‘effectorderingfordata display’(FriendlyandKwan,). Inthe s,thesystematic collection andstudyofsocial data beganinvarious Europeancountries,undertherubricof‘politicalarithmetic’(JohnGrauntnd ,a William Petty, ),with thegoals ofinforming the state about mattersrelated to  wealth,population,agriculturalland,taxesandsoforth, aswellasforcommercial purposessuchasinsuranceandannuitiesbasedonlifetables(JandeWitt,).At approximatelythesametime,theinitialstatementsofprobabilitytheoryaround (seeBall,)togetherwiththeideaofcoordinatesystemswereappliedbyChris-  tiaanHuygensintogivethefirstgraphofacontinuousdistributionfunction (fromGraunt’sbasedonthebillsofmortality).hemid-wsstahefirstbivariate plotderivedfromempiricaldata,atheoreticalcurverelatingbarometricpressureto  altitude, andthefirstknownweather m sho ap,wingprevailing windsonamapof theearth(Halley,). Bytheendofthiscentury,thenecessaryelementsforthedevelopmentofgraphical methodswereathand–somerealdataofsignificantinterest,sometheorytomake  For navigation, latitude could be fixed from star inclinations, but longitudeuirreed q ac- curatemeasurementoftimeatsea,anunsolved problemuntilwith the ntioinnveof amarinechronometerbyJohnHarrison.SeeSobel()forapopularaccount.  Forexample,Graunt()usedhistabulationsofLondonbirthsanddearotm hpa sfrish recordsandthebillsofmortalitytoestimatethenumberofmenthekingwouldfindavail- ableintheeventofwar(Klein,,pp.–).  Image:http://math.yorku.ca/SCS/Gallery/images/huygens-graph.gif  Image:http://math.yorku.ca/SCS/Gallery/images/halleyweathermap-.jpg22 MichaelFriendly senseofthem,andafewideasfortheirvisualrepresentation. Perhapsmoreimpor- tantly,onecanseethiscenturyasgivingrisetothebeginningsofvisualthinking,as illustratedbytheexamplesofScheinerandvanLangren. 1.2.3 1700–1799:NewGraphicForms Withsomerudimentsofstatistical theory,dataofinterestandimportance,andthe idea of graphic representation at least somewhatestablished, the th century wit- nessed the expansion of these aspects to new domains and new graphic forms. In cartography,mapmakersbegantotrytoshowmorethanjustgeographicalposition onamap.Asaresult,newdatarepresentations(isolinesandcontos)uwrereinvented, andthematicmappingofphysicalquantitiestookroot.Towardstheendofthiscen- tury, we see the first attempts at the thematic mapping of geologic, economic and medicaldata. Abstractgraphs,andgraphsoffunctionsbecamemorewidespreaong d,alwiththe earlystirringsofstatisticaltheory(measurementerror)andsystematiccollectionof empirical data. Asother (economicand political) data begantobleecctoled,some novel visual forms were invented to portray them, so the data could ‘speak to the eyes.’ Forexample,theuseofisolinestoshowcontoursofequalvalueonacoordinate grid(mapsandcharts)wasdevelopedbyEdmundHalley().Figure.,showing isogons–linesofequal magnetic declination –isamong thefirstexamples ofthe- maticcartography,overlayingdataonamap.Contourmapsandtgorap pohicmaps wereintroducedsomewhatlaterbyPhilippeBuache()andMarcellinduCarla- Boniface(). Timelines, or ‘cartes chronologiques,’ were first introduced baycqu J es Barbeu- Dubourgintheformofanannotatedchartofallofhistory(fromCreation)ona- footscroll(Ferguson,).JosephPriestley,presumablyindependently,usedarmeo convenientformtoshowfirstatimelinechartofbiography(lifespansoffamous people,B.C.toA.D.,Priestley,),andthenadieletdachartofhistory (Priestley,). heuseofgeometricfigures(squaresorrectangles)andcartogramstocomparear-  easordemographicquantitiesbyCharlesdeFourcr( oy)andAugustF.W.Crome ()providedanother novelvisualencodingforquantitativeaduastingsuperim- posedsquarestocomparetheareasofEuropeanstates. Aswell,severaltechnologicalinnovationsprovidednecessaryingredientsforthe productionanddisseminationofgraphicworks.Someoftheseiftaactiledtherepro- ductionofdataimages,suchasthree-colour printing, invented byJacobleBlonin ,andlithography, inventedbyAloysSenefelderin.Ofthelatter,Robinson (,p.)says“theeffectwasasgreatastheintroductionofthe machine Xerox .” Yet,likelyduetoexpense,mostofthesenewgraphicformsapedpeianrpublications withlimitedcirculation,unlikelytoattractwideattention.  Image:http://math.yorku.ca/SCS/Gallery/images/palsky/defourcroy.jpg

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