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Scien&ficandLargeDataVisualiza&on22November2017
HighDimensionalData
MassimilianoCorsiniVisualCompu,ngLab,ISTI-CNR-Italy
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Overview
• GraphsExtensions• Glyphs
– ChernoffFaces– Mul&-dimensionalIcons
• ParallelCoordinates• StarPlots• DimensionalityReduc&on
– PrincipalComponentAnalysis(PCA)– LocallyLinearEmbedding(LLE)– IsoMap– t-SNE
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Mul,-setBarCharts
• Alsocalledgroupedbarcharts.
• Likebarchartformoredatasets.
• Allowaccuratenumericalcomparisons.
• Itcanbeusedtoshowmini-histograms.
Figure from Data Visualization Catalogue.
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Mul,pleBars
• Distribu,onsofeachvariableamongthedifferentcategories/datapoints.
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Mul,pleViews
• Distribu,onsofeachvariableamongthedifferentcategories/datapoints(eachvariablehasitsowndisplay).
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StackedBarCharts
• Eachdatasetisdrawnontopofeachother.
• Twotypes:– SimpleStackedBarCharts– PercentageStackedBarCharts.
• Moresegmentseachbarmoredifficulttoread.
Figure from Data Visualization Catalogue.
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SimplevsPercentageBarCharts
• SimpleStackedBarCharts– Usefulifthevisualiza,onoftheabsolutevalues(andtheirsum)ismeaningful.
• PercentageBarCharts– BeRertoshowtherela,vedifferencesbetweenquan,,esinthedifferentgroups.
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Spineplots
• Generaliza,onofstackedbarcharts.• Specialcaseofmosaicplot.• Permittoshowbothpercentagesandpropor,onsbetweenvariables.
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Spineplots–Example
• Cardata:
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Spineplots–Example
Figure from Information Visualization Course, Università Roma 3.
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Spineplots–Example
Figure from Information Visualization Course, Università Roma 3.
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Spineplots–Example
• Conveybothpercentagesandpropor,ons.
Figure from Information Visualization Course, Università Roma 3.
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MosaicPlots
• Theygiveanoverviewofthedatabyvisualizingtherela,vepropor,ons.
• AlsoknownasMekkocharts.
Figure by Seancarmody under CC-BY-SA 3.0.
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MosaicPlots
• Titanicdata(fromWikipedia):
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MosaicPlots
• Variablegenderàver,calaxis.
Figure from Information Visualization Course, Università Roma 3.
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MosaicPlots
• AddvariableClassàHorizontalaxis.
Figure from Information Visualization Course, Università Roma 3.
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MosaicPlots
• Addvariablesurvivedàver,calaxis.
Figure from Information Visualization Course, Università Roma 3.
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Figure from Information Visualization Course, Università Roma 3.
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MosaicPlots
• Advantages:– Maximaluseoftheavailablespace– Goodoverviewofthepropor,onsbetweendata– Goodoverviewofthevariabledependency
• Disadvantages:– Extensiontomanyvariablesisdifficult
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TreeMaps
• Analterna,vewaytovisualizeatreedatastructure.
• Space-efficient(!)• Thewayrectanglesaredividedandorderedintosub-rectanglesisdependentonthe,lingalgorithmused.
Figure from Data Visualization Catalogue.
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TreeMaps–Example
Figure from Data Visualization Catalogue.
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CushionTreemaps• Usesuitableshadingtorevealthefinestructureofthehierarchy.
Figure from Jarke J. van Wijk Huub van de Wetering,“Cushion Treemaps: Visualization of Hierarchical Information”, InfoVis’99.
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CushionTreemaps• Shadingfunc,on–1Dcase:
Figure from Jarke J. van Wijk Huub van de Wetering,“Cushion Treemaps: Visualization of Hierarchical Information”, InfoVis’99.
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CushionTreemaps
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SquarifiedTreemaps
Figure from Mark Bruls, Kees Huizing, and Jarke J. vanWijk, “Squarified Treemaps”, Proc. Joint Eurographics and IEEE TCVG Symp. on Visualization.
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SquarifiedTreemaps
Figure from Mark Bruls, Kees Huizing, and Jarke J. vanWijk, “Squarified Treemaps”, Proc. Joint Eurographics and IEEE TCVG Symp. on Visualization.
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ScaRerPlotMatrix(SPLOM)
• Eachpossiblepairofvariablesisrepresentedinastandard2DscaRerplot.
• Manyworksinliteraturetofindefficientwaytopresentthem.
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SPLOM
Figure from R-Blogger.
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ChernoffFaces
• IntroducedbyHermanChernoffin1973.• Weareverygoodatrecognizefaces.• Variablesaremappedonfacialfeatures:– Width/curvatureofmouth– Ver,calsizeoftheface– Size/slant/separa,onofeyes– Sizeofeyebrows– Ver,calposi,onofeyebrows
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ChernoffFaces(lawyersjudge)
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ChernoffFaces
• Chernofffacesreceivedsomecri,cism– Difficulttocompare.– Alegendisnecessary.
• Moreover,themappingshouldbechoosecarefullytoworkproperly.
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Mul,-dimensionalIcons• SpenceandParr(1991)proposedtoencodeproper,esofanobjectinsimpleiconicrepresenta,onandassemblethemtogether.
• Theyappliedthisapproachtocheckquicklydwelloffers.
Robert Spence and Maureen Parr, “Cognitive assessment of alternatives”, Interacting with Computers 3, 1991.
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SpenceandParr(1991)(examples)
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PetalsasaGlyph
• TheideaofMoritzStefanertovisualizealifeindexistomapseveralvariablesintopetalsofdifferentsize.
• Website:www.oecdbeRerlifeindex.org
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ParallelCoordinates
• OriginallyaRributedtoPhilbertMauriced'Ocagne(1885).
• ExtendsclassicalCartesianCoordinatesSystemtovisualizemul,variatedata.
• Re-discoveredandpopularizedbyAlfredIsenbergin1970s.
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ParallelCoordinatesTwovariables
X Y
X
Y
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ParallelCoordinatesThreevariables
X Y Z X
Y
Z
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ParallelCoordinatesFourVariables
X Y Z
X
Y
Z
W
W
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ParallelCoordinatesNvariables
Figure from G. Palmas, M. Bachynsky, A. Oulasvirta, Hans Peter Seidel, T. Weinkauf, “An Edge-Bundling Layout for Interactive Parallel Coordinates“, in PacificVis 2014.
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AxisOrder
• Orderoftheaxesplayafundamentalroleinreadability.
• Butwehaven!combina,ons.
• Trybyyourselfatthiswebsite.• Manystrategieshavebeeninves,ga,ngforaxesre-ordering.
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Re-orderingandEdge-bundling
Figure from G. Palmas, M. Bachynsky, A. Oulasvirta, Hans Peter Seidel, T. Weinkauf, “An Edge-Bundling Layout for Interactive Parallel Coordinates“, in PacificVis 2014.
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Illustra,veRenderingandParallelCoordinates
Figure from K. T. McDonnell and K. Mueller, “Illustrative Parallel Coordinates“, in Computer Graphics Forum, vol. 27, no. 3, pp. 1031-1038, 2008.
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StarPlot• Knownwithmanynames:radarchart,spiderchart,webchart,etc.
• Analogoustoparallelcoordinates,buttheaxesareposi,onedinpolarcoordinates(equi-angular).
• Posi,onofthefirstaxisisuninforma,ve.
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StarPlot
• Easytocompareproper,esofaclassofobjectsoracategory.
• Noteasytounderstandtrade-offbetweendifferentvariables.
• Notsuitableformanyvariablesormanydata.
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StarPlot
• Example:measurethequalityofaphotograph.
Figure from T. O. Aydın, A. Smolic and M. Gross, "Automated Aesthetic Analysis of Photographic Images“, in IEEE Transactions on Visualization and Computer Graphics, vol. 21, no. 1, pp. 31-42.
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Summary
• Manysolu,onsexists(arecentsurveycitesmorethan250papers).
• Wehaveseensomeofthemostfamousmethods(e.g.SPLOM,parallelcoordinates).
• Nextlessonwewillfocusondimensionalityreduc,on.
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Ques&ons?