Scien&ficandLargeDataVisualiza&on22November2017
HighDimensionalData
MassimilianoCorsiniVisualCompu,ngLab,ISTI-CNR-Italy
Overview
• GraphsExtensions• Glyphs
– ChernoffFaces– Mul&-dimensionalIcons
• ParallelCoordinates• StarPlots• DimensionalityReduc&on
– PrincipalComponentAnalysis(PCA)– LocallyLinearEmbedding(LLE)– IsoMap– t-SNE
Mul,-setBarCharts
• Alsocalledgroupedbarcharts.
• Likebarchartformoredatasets.
• Allowaccuratenumericalcomparisons.
• Itcanbeusedtoshowmini-histograms.
Figure from Data Visualization Catalogue.
Mul,pleBars
• Distribu,onsofeachvariableamongthedifferentcategories/datapoints.
Mul,pleViews
• Distribu,onsofeachvariableamongthedifferentcategories/datapoints(eachvariablehasitsowndisplay).
StackedBarCharts
• Eachdatasetisdrawnontopofeachother.
• Twotypes:– SimpleStackedBarCharts– PercentageStackedBarCharts.
• Moresegmentseachbarmoredifficulttoread.
Figure from Data Visualization Catalogue.
SimplevsPercentageBarCharts
• SimpleStackedBarCharts– Usefulifthevisualiza,onoftheabsolutevalues(andtheirsum)ismeaningful.
• PercentageBarCharts– BeRertoshowtherela,vedifferencesbetweenquan,,esinthedifferentgroups.
Spineplots
• Generaliza,onofstackedbarcharts.• Specialcaseofmosaicplot.• Permittoshowbothpercentagesandpropor,onsbetweenvariables.
Spineplots–Example
• Cardata:
Spineplots–Example
Figure from Information Visualization Course, Università Roma 3.
Spineplots–Example
Figure from Information Visualization Course, Università Roma 3.
Spineplots–Example
• Conveybothpercentagesandpropor,ons.
Figure from Information Visualization Course, Università Roma 3.
MosaicPlots
• Theygiveanoverviewofthedatabyvisualizingtherela,vepropor,ons.
• AlsoknownasMekkocharts.
Figure by Seancarmody under CC-BY-SA 3.0.
MosaicPlots
• Titanicdata(fromWikipedia):
MosaicPlots
• Variablegenderàver,calaxis.
Figure from Information Visualization Course, Università Roma 3.
MosaicPlots
• AddvariableClassàHorizontalaxis.
Figure from Information Visualization Course, Università Roma 3.
MosaicPlots
• Addvariablesurvivedàver,calaxis.
Figure from Information Visualization Course, Università Roma 3.
Figure from Information Visualization Course, Università Roma 3.
MosaicPlots
• Advantages:– Maximaluseoftheavailablespace– Goodoverviewofthepropor,onsbetweendata– Goodoverviewofthevariabledependency
• Disadvantages:– Extensiontomanyvariablesisdifficult
TreeMaps
• Analterna,vewaytovisualizeatreedatastructure.
• Space-efficient(!)• Thewayrectanglesaredividedandorderedintosub-rectanglesisdependentonthe,lingalgorithmused.
Figure from Data Visualization Catalogue.
TreeMaps–Example
Figure from Data Visualization Catalogue.
CushionTreemaps• Usesuitableshadingtorevealthefinestructureofthehierarchy.
Figure from Jarke J. van Wijk Huub van de Wetering,“Cushion Treemaps: Visualization of Hierarchical Information”, InfoVis’99.
CushionTreemaps• Shadingfunc,on–1Dcase:
Figure from Jarke J. van Wijk Huub van de Wetering,“Cushion Treemaps: Visualization of Hierarchical Information”, InfoVis’99.
CushionTreemaps
SquarifiedTreemaps
Figure from Mark Bruls, Kees Huizing, and Jarke J. vanWijk, “Squarified Treemaps”, Proc. Joint Eurographics and IEEE TCVG Symp. on Visualization.
SquarifiedTreemaps
Figure from Mark Bruls, Kees Huizing, and Jarke J. vanWijk, “Squarified Treemaps”, Proc. Joint Eurographics and IEEE TCVG Symp. on Visualization.
ScaRerPlotMatrix(SPLOM)
• Eachpossiblepairofvariablesisrepresentedinastandard2DscaRerplot.
• Manyworksinliteraturetofindefficientwaytopresentthem.
SPLOM
Figure from R-Blogger.
ChernoffFaces
• IntroducedbyHermanChernoffin1973.• Weareverygoodatrecognizefaces.• Variablesaremappedonfacialfeatures:– Width/curvatureofmouth– Ver,calsizeoftheface– Size/slant/separa,onofeyes– Sizeofeyebrows– Ver,calposi,onofeyebrows
ChernoffFaces(lawyersjudge)
ChernoffFaces
• Chernofffacesreceivedsomecri,cism– Difficulttocompare.– Alegendisnecessary.
• Moreover,themappingshouldbechoosecarefullytoworkproperly.
Mul,-dimensionalIcons• SpenceandParr(1991)proposedtoencodeproper,esofanobjectinsimpleiconicrepresenta,onandassemblethemtogether.
• Theyappliedthisapproachtocheckquicklydwelloffers.
Robert Spence and Maureen Parr, “Cognitive assessment of alternatives”, Interacting with Computers 3, 1991.
SpenceandParr(1991)(examples)
PetalsasaGlyph
• TheideaofMoritzStefanertovisualizealifeindexistomapseveralvariablesintopetalsofdifferentsize.
• Website:www.oecdbeRerlifeindex.org
ParallelCoordinates
• OriginallyaRributedtoPhilbertMauriced'Ocagne(1885).
• ExtendsclassicalCartesianCoordinatesSystemtovisualizemul,variatedata.
• Re-discoveredandpopularizedbyAlfredIsenbergin1970s.
ParallelCoordinatesTwovariables
X Y
X
Y
ParallelCoordinatesThreevariables
X Y Z X
Y
Z
ParallelCoordinatesFourVariables
X Y Z
X
Y
Z
W
W
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.
AxisOrder
• Orderoftheaxesplayafundamentalroleinreadability.
• Butwehaven!combina,ons.
• Trybyyourselfatthiswebsite.• Manystrategieshavebeeninves,ga,ngforaxesre-ordering.
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.
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.
StarPlot• Knownwithmanynames:radarchart,spiderchart,webchart,etc.
• Analogoustoparallelcoordinates,buttheaxesareposi,onedinpolarcoordinates(equi-angular).
• Posi,onofthefirstaxisisuninforma,ve.
StarPlot
• Easytocompareproper,esofaclassofobjectsoracategory.
• Noteasytounderstandtrade-offbetweendifferentvariables.
• Notsuitableformanyvariablesormanydata.
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.
Summary
• Manysolu,onsexists(arecentsurveycitesmorethan250papers).
• Wehaveseensomeofthemostfamousmethods(e.g.SPLOM,parallelcoordinates).
• Nextlessonwewillfocusondimensionalityreduc,on.
Ques&ons?