Angular Brushing of ExtendedParallel Coordinates

Helwig Hauser, FlorianLedermann,andHelmutDoleischHauser@VRVis.at, flo@subnet.at, andDoleisch@VRVis.at

VRVis ResearchCenterin Vienna,Austria,http://www.VRVis.at/vis/

Abstract

In this paper we present angularbrushingfor parallel coor-dinates (PC) as a new approach to high-light rational data-properties, i.e., features which depend on two data dimen-sions (instead of one). We also demonstrate smoothbrush-ing of PC as an intuitive tool to specify non-binary degree-of-interest functions (then used for F+C visualization). Wealso shortly describe our implementation as well as its ap-plication to the visualization of CFD data.

Keywords: information visualization, parallel coordinates,brushing, linear correlations, focus+context visualization

1. Intr oductionFor many yearsalready, parallelcoordinates(PC)[5, 4] arewell-known andanoftenusedtechniquein informationvi-sualization(InfoViz). Multi-dimensionaldata-setsarevisu-alizedby drawing onepoly-line for every data-pointacrosscoordinateaxeswhich arelaid out in parallel,side-by-side.Thepoly-linesintersectthecoordinateaxesatpointswhichcorrespondto the respective componentsof the particulardata-vector. Thereby, up to a dozenof datadimensions(orevenmore)arewell visualized,especiallywhenthevisual-ization is combinedwith proper interactionfeaturessuchas real-time re-orderingof coordinateaxes or interactivebrushingin singledimensions[7].

Brushing. As alreadymentioned,brushingis a veryeffec-tive techniquefor specifyinganexplicit focusduringinfor-mationvisualization[1, 9]. Theuseractivelymarkssub-setsof thedata-set,for example,by usinga brush-like interfaceelement.If usedin conjunctionwith multiple linkedviews,brushingcanenableusersto understandcorrelationsacrossmultipledimensions[1].

Focus+contextvisualization. Brushingalsois veryusefulto steeradrill-down into thevisualizationof reallybig data-sets– by specifyinga (limited and limiting) focus, moredetailscanbe shown for the selecteddata-points.This re-lates to anothervery important InfoViz conceptwhich isfocus-plus-context (F+C) visualization[3]. The basicideaof F+Cvisualizationis to jointly visualizehighly interesting

Figure 1. Reading between the lines: whereasmost of the poly-lines have a pos. slope betweenthe 2nd and the 3rd axis, just a few don’t – thosehave been emphasized using angular brushing.

partsof thedatain detail aswell asthe restof thedata-setin reducedstyle,for orientationandimprovednavigation.

Degree-of-interestfunctions. For specifyingwhich partsof thedataareto bedrawn in detail, i.e., for specifyingthefocus,a degree-of-interest(DOI) function is used[3], usu-ally assigninga valueof 1 or 0 to eachdata-point,depend-ing on whetherthe data-pointis of currentinterestor not.Brushingis aneffective methodto actively (andexplicitly)assignvaluesof

�to data-pointsof interest[1, 10].

Brushing extensions. In addition to standardbrushing,several usefulextensionshave beenproposedin literature.The introduction of compositebrushes[7], for example,enabledusersto morespecificallydefinetheir focus. Thecombinationof brushingandnon-binaryDOI functions[7]proved to be useful for data-setswith gradualchangesintheir dataattributes,for example,datafrom scientificsimu-lation [2].

In this paper, we demonstrateseveralsmall but very ef-fective extensionsto brushingas an interactiontechniquefor parallel coordinates(like angular brushing or smooth

Figure 2. Extended parallel coordinates, a sample view of the cars data-set: cars with six cylinders wereemphasized through brushing, histograms are laid over axes, and one data-point is shown with all details.

brushing). Theremainderof this paperis structuredasfol-lows: first we presenttwo extensionsof brushingfor PC(section2). Afterwards,weshortlypresentsomeimplemen-tation issues(section3). The applicationitself andsomeresultsfrom visual dataanalysisaredemonstratedin sec-tion 4.

2. ExtendedBrushing for Parallel CoordinatesAs alreadymentionedabove, brushingeffectively enablesthe userto (explicitely) specifyhis or her focus. In paral-lel coordinates,this usually is accomplishedby markingacertaindatasub-setof interestaccordingto valueswithin asingledatadimension.In thecars data-set[8], for example,a usercould focuson carswith six cylindersby brushingtherespectiveportionof thecylinders-axis(cf. Fig. 2).

In our application of visually investigating multi-dimensionaldata-setsoriginatingin aphysically-basedsim-ulationof dynamicprocessesbasedon computationalfluiddynamics(CFD), we found standardbrushingof PC veryuseful,however, we neededto go further. Therequirementwasto specifyafocusnotonly in dependenceof onedataat-tribute(onedimension),but to dosowith respectto at leasttwo of them– likebrushingall thosedata-pointswhich fea-turea � -velocity larger thantherespective � -velocity. Theconsequencewas to introducea new brushingtechniquewhichwe call angular brushing.

2.1. Angular Brushing of Parallel Coordinates

Onestrengthof PC is its effectivenessof visualizingrela-tionsbetweencoordinateaxes. Bringing axesnext to eachotherin aninteractiveway, theusercaninvestigatehow val-uesarerelatedto eachotherwith specialrespectto two ofthedatadimensions.Thisway, it is notonly possibleto see

whetherdata-pointsexhibit high or low valuesin singledi-mensions,but alsotheir relationcanbe understood.Morespecifically, the slopeof the line-segmentsin-betweentwoaxes tells the user, whetherthereis a positive or negativecorrelationin-betweenvalues(of courseassumingthat theusersetup a propermapping). Outliersalsocanbe easilyfoundwith respectto two datadimensions– whenall but afew line-segmentshaveapositiveslope,thenthefew othersclearlystandout (seeFig. 1 for anillustration).

In thispaper, wedemonstratehow thisfeatureof PCeas-ily can be exploited for an extendedbrushingtechnique,i.e., angularbrushing. In addition to standardbrushing,which primarily actsalong the (parallel) axes, we enablethespacein-betweenaxesfor brushinginteraction,aswell.Theusercaninteractively specifyasub-setof slopeswhichthenyieldsall thosedata-pointsto bemarkedaspartof thecurrentfocus.SeeFig. 1 for anexample,whereall negativeslopeshavebeenmarkedbetweenthesecondandthird axis.

Angular brushingasdescribedabove is a usefulexten-sion to PC, also becauseit very well correspondsto theeffective visual cues provided by PC. Inherently, angu-lar brushingopensthe extendedfield of brushingmulti-dimensionalpropertiesof high-dimensionaldata-sets. Inadditionto compositebrusheswhich arecomposedmulti-ple single-axisbrushesby theuseof logical operators,an-gularbrushesallow theselectionof rationalpropertieswithrespectto two of the datadimensions.Whencomparedtocompositebrushesby theuseof a scatterplotvisualization,weclearlyseethatbrushesbasedonlogicaloperatorsselectsub-setswhich arealignedwith the displayaxes,whereasangularbrushesselectsub-setswhich arealignedwith thediagonalswhenvisualizedin a scatter-plot (seealsoFig. 3for comparison).

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——— composite brushes ——— ——— angular brushes ———

AND-brush OR-brush angular brush angular brush,after axis flipping

Figure 3. Comparing composite brushes (on the left) and angular brushes (on the right), using PC (top row)and scatterplots (bottom row): composite brushes address “horizontal/vertical” features, whereas angularbrushes emphasize “diagonal” feature.

Figure 4. Linking and brushing, an example: in a scatter-plot (shown on the left side), smooth brushingwas used to mark data-points of low pressure and low velocity; a linked 3D view (on the top right) shows thesame data with the brushed data-points high-lighted; thirdly, the PC view (on the lower right) also shows thesame data, also high-lighting the brushed sub-set.

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2.2. SmoothBrushing and Non-Binary DOIs

Many well-known F+C techniquesin InfoViz suchasfish-eye views [3], for example,do not usea discretedistinc-tion betweenfocusandcontext, but allow amulti-valuedoreven continuoustransition,which inherentlysupportsthementalconnectionbetweendata-pointsin focus and theircontext. This correspondsto a degree-of-interestfunction,whichnon-binarilymapsinto the � ��� ��� -range.

Brushing easily combineswith non-binaryDOI func-tions [7], i.e., whensmoothlydelimitedbrushesareused.Thereby, at thebrushboundaries,fractionalDOI-valuesareassigned.Whencompositebrushesarecomposedthroughtheuseof logical operators,fuzzy logic is employedto ag-gregatefinal DOI-valuesfor everysingledata-point.

In conjunctionwith PCweextendtheinteractively spec-ified brushby a certain,user-definedpercentageto accom-modatea smoothgradientof DOI-valuesat its borders.Whencombiningsmoothbrushesthroughlogicaloperators,weapplytheŁukasiewicz norm,known from fuzzy logic asa comparablylargenorm[6], i.e., a normwhich (whenap-plied repeatedly)only slowly convergesto � andthereforebetterconservesthetransitionalDOI-gradients.

3. ImplementationTo dealwith real-world data-sets– in our caseconsistingof

� � – � ��� data-pointseach– we quickly experiencedthelimitations of a brute-forceimplementationof parallelco-ordinates.Especiallyaswe alsoneededsemi-transparency,coloring,andanti-aliasedline-segments,loadis highon thegraphicshardwareduringPCvisualization.

In the following, we shortly describesomeof the ap-proacheswe utilized to still provide real-time response:(1.) Coherenceis exploited during interactionby re-usingasmuchvisual outputaspossible. If oneaxis is modifiedduringinteraction,for example,lines-segmentsareonly re-drawn locally. (2.) Progressive renderingprovides imme-diate feed-backthrougha preview-style of rendering,i.e.,withoutanti-aliasingor semi-transparency. As soonasthereis time,high-qualityresultsarecomputed.(3.) Bi-threadedimplementationde-couplesrenderingandinteraction.Onethreadserves the userinterfaceandguaranteesinteractiveresponse,while theotherthreaddealswith rendering.

4. Application and ResultsIn our applicationwe investigatemulti-dimensionaldata-setswhich originatein CFD simulationswith a dozenofdatadimensions,or more. During flow simulation,valueslike temperature,pressure,velocity, aswell asothers,arecomputedfor all cellswithin a detailedCFDgrid.

Parallel coordinatesproved to be very useful for datainvestigation. The interactive characterof the here de-scribedimplementationallows for fastandflexible dataex-ploration,evenwhensimultaneouslyinvestigatingmultiple

dimensions.Linking PC andother typesof views (like a3D SciViz view, cf. Fig. 4, topright) andusingourbrushingfeatureseaseddataexploration.Also thecombinationwithscatter-plotswasfoundto beuseful,primarily becausecom-positebrushesarespecifiedmoreeasilyin a scatter-plot.

Figs.3 andespecially4 show resultsof dataexplorationby theuseof PC.Thedatashown is theresultof a simula-tion of flow throughpipesshapedasa T-junction. Flow iscomingfrom theleft andthetop (Fig. 4, top left).

5. Summary and ConclusionsIn this paper, we havepresentedangular brushing asanewtechniqueto effectively selectdatasub-setswhichexhibit adatacorrelationalong(at least)two axes. We alsoshowedhow smooth brushing can be used,even in combinationwith composite brushes. Moredetails,moreimages,ashortvideo,aswell asa longertechnicalreportareavailableviahttp://www.VRVis.at/vis/.

We concludethattheworth of a visualizationby theuseof parallel coordinatesincreasesdrasticallywhen interac-tion featureslike axisre-ordering,etc.,areadded.

Acknowledgements.As (partially)beingpartof VRVis’ basicre-searchonvisualization(http://www.VRVis.at/vis/), thiswork alsowasfundedby K plus (http://www.kplus.at/).The authorsalso thankAVL.com for providing dataaswell asRobertKosarafor his valuablehints.

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