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?