Angular Brushing of Extended Parallel Coordinates2.1. Angular Brushing of Parallel Coordinates One...
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Angular Brushing of Extended Parallel Coordinates Helwig Hauser, Florian Ledermann, and Helmut Doleisch [email protected], [email protected], and [email protected] VRVis Research Center in Vienna, Austria, http://www.VRVis.at/vis/ Abstract In this paper we present angular brushing for 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 smooth brush- ing of PC as an intuitive tool to specify non-binary degree- of-interest functions (then used for F+C visualization). We also 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. Introduction For many years already, parallel coordinates (PC) [5, 4] are well-known and an often used technique in information vi- sualization (InfoViz). Multi-dimensional data-sets are visu- alized by drawing one poly-line for every data-point across coordinate axes which are laid out in parallel, side-by-side. The poly-lines intersect the coordinate axes at points which correspond to the respective components of the particular data-vector. Thereby, up to a dozen of data dimensions (or even more) are well visualized, especially when the visual- ization is combined with proper interaction features such as real-time re-ordering of coordinate axes or interactive brushing in single dimensions [7]. Brushing. As already mentioned, brushing is a very effec- tive technique for specifying an explicit focus during infor- mation visualization [1, 9]. The user actively marks sub-sets of the data-set, for example, by using a brush-like interface element. If used in conjunction with multiple linked views, brushing can enable users to understand correlations across multiple dimensions [1]. Focus+context visualization. Brushing also is very useful to steer a drill-down into the visualization of really big data- sets – by specifying a (limited and limiting) focus, more details can be shown for the selected data-points. This re- lates to another very important InfoViz concept which is focus-plus-context (F+C) visualization [3]. The basic idea of F+C visualization is to jointly visualize highly interesting Figure 1. Reading between the lines: whereas most of the poly-lines have a pos. slope between the 2 nd and the 3 rd axis, just a few don’t – those have been emphasized using angular brushing. parts of the data in detail as well as the rest of the data-set in reduced style, for orientation and improved navigation. Degree-of-interest functions. For specifying which parts of the data are to be drawn in detail, i.e., for specifying the focus, a degree-of-interest (DOI) function is used [3], usu- ally assigning a value of 1 or 0 to each data-point, depend- ing on whether the data-point is of current interest or not. Brushing is an effective method to actively (and explicitly) assign values of to data-points of interest [1, 10]. Brushing extensions. In addition to standard brushing, several useful extensions have been proposed in literature. The introduction of composite brushes [7], for example, enabled users to more specifically define their focus. The combination of brushing and non-binary DOI functions [7] proved to be useful for data-sets with gradual changes in their data attributes, for example, data from scientific simu- lation [2]. In this paper, we demonstrate several small but very ef- fective extensions to brushing as an interaction technique for parallel coordinates (like angular brushing or smooth
Transcript of Angular Brushing of Extended Parallel Coordinates2.1. Angular Brushing of Parallel Coordinates One...
Angular Brushing of ExtendedParallel Coordinates
Helwig Hauser, FlorianLedermann,[email protected], [email protected], [email protected]
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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