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Clustering:AnExampleExperiment
Researcherswereinterestedinstudyinggeneexpressionpatternsindevelopingsoybeanseeds.
Seedswereharvestedfromsoybeanplantsat25,30,40,45,and50daysafterflowering(daf).
OneRNAsamplewasobtainedforeachlevelofdaf.
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AnExampleExperiment(continued)
Eachofthe5sampleswasmeasuredontwotwo-colorcDNAmicroarrayslidesusingaloopdesign.
Theentireprocesswerepeatedonasecondoccasiontoobtainatotaloftwoindependentbiologicalreplications.
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Rep1
Rep2
DiagramIllustratingtheExperimentalDesign
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Thedafmeansestimatedforeachgenefromamixedlinearmodelanalysisprovideausefulsummaryofthedataforclusteranalysis.
NormalizedDataforOneExampleGene
daf
daf
NormalizedLogSignal
EstimatedMeans+or–1SE
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400genesexhibitedsignificantevidenceofdifferentialexpressionacrosstime(p-value<,FDR=%).Wewillfocusonclusteringtheirestimatedmeanprofiles.
NormalizedDataforOneExampleGene
daf
daf
NormalizedLogSignal
EstimatedMeans+or–1SE
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Webuildclustersbasedonthemostsignificantgenesratherthanonallgenesbecause...
Muchofthevariationinexpressionisnoiseratherthanbiologicalsignal,andwewouldrathernotbuildclustersonthebasisofnoise.
Someclusteringalgorithmswillbecomecomputationallyexpensiveiftherearealargenumberofobjects(geneexpressionprofilesinthiscase)tocluster.
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EstimatedMeanProfilesforTop36Genes
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DissimilarityMeasures
Whenclusteringobjects,wetrytoputsimilarobjectsinthesameclusteranddissimilarobjectsindifferentclusters.
Wemustdefinewhatwemeanbydissimilar.
Therearemanychoices.
Letxandydenotemdimensionalobjects:
x=(x1,x2,...,xm)y=(y1,y2,...,ym)
.,estimatedmeansatm=5fivetimepoints
foragivengene.
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ParallelCoordinatePlots
Scatterplot
x1
x2
ParallelCoordinatePlot
Coordinate
Value
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