MathematicalModeling

Lecture1Instructor:LiangfuLuliangfulv@

Multi-DimensionalDataVisualization

---ParallelCoordinates2Multi-DimensionalDataVisualizinglargeinformationspacethroughrelativelysmallwindowscreen.Visualizingmulti-dimensionaldata(n>3)in2Dspace.

3Axisreconfigurationtechniques,suchasparallelcoordinatesandglyphs;Dimensionalsubsetting,suchasscatterplotmatrices4parallelcoordinatesglyphsscatterplotmatricesParallelCoordinatesGlyphsScatterplotMatrices5

Background

Proposedin1985byAlfredInsellbergGoodformulti-dimensionaldataexplorationWidelyusedininformationvisualizationofmulti-dimensionaldata6TorepresentNdimensionaldataSetNequidistantverticalaxesinparallelEachaxisscaledto[min,max]rangeofattributesPutdatatointersectsoncorrespondingaxesConnectintersectsExample:(0,1,-1,2)7

Rationale

Cartesianvs.Paralleloordinates

Example1:DatasetinaCartesiancoordinateSamedatasetinparallelcoordinates8Example2:AirtrafficcontrolCartesianCoordinatesParallelCoordinates910

GoodExample

ParallelCoordinates:Advantages

Multi-dimensionaldatacanbevisualizedintwodimensionalspacewithlowcomplexity.Eachvariableistreateduniformly.Relationswithinmulti-dimensionaldatacanbediscovered(“datamining”).1112

BadExamplesParallelCoordinates:DisadvantagesAxesaretoocloseasdimensionsincrease.Cluttercanreduceperceivedinformation.Varyingtheorderofaxesscale,althoughindicatingdifferentpatterns,maycauseconfusion.13ParallelCoordinatesVisualizationSummaryEachdatapointismappedtoaline(Duality)Similarpointscorrespondtosimilarlines(Correlation)Effectiveexplorationandclustering(Pattern)Problems:orderofaxes,limitto1~20dimensions14IndividualAssignment:VisualizingIrisDataIrissetosaIrisversicolorIrisvirginica15TeamWork:ImprovingParallelCoordinatesReferencesInselberg,A.,Theplanewithparallelcoordinates.TheVisualComputer,1985.1(2):p.69-91.Wegman,E.J.,HyperdimensionalDataAnalysisUsingParallelCoordinates.JournaloftheAmericanStatisticalAssociation,1990.85(411):p.664-675.Bertini,E.,A.Tatu,andD.Keim,QualityMetricsinHigh-DimensionalDataVisualization:AnOverviewandSystematization.IEEETransactionsonVisualizationandComputerGraphics,2011.17(12):p.2203-2212.Dasgupta,A.andR.Kosara,Pargnostics:Screen-SpaceMetricsfo