外文资料--A Co-clustering Technique for Gene Expression.PDF外文资料--A Co-clustering Technique for Gene Expression.PDF

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ACOCLUSTERINGTECHNIQUEFORGENEEXPRESSIONDATAUSINGBIPARTITEGRAPHAPPROACHSUVENDUKANUNGODEPTOFCOMPSCBITMESRA,RANCHIALLHABADCAMPUS,UP,INDIAFKANUNGOREDIFFCOMGADADHARSAHOODEPTOFITMCABITMESRA,RANCHIJHARKHAND,INDIAGSAHOOBITMESRAACINMANOJMADHAVAGOREDEPTOFCOMPSCENGGMNNITALLAHABAD,UP,INDIAGOREMNNITACINABSTRACTMININGMICROARRAYDATASETSISVITALINBIOINFORMATICSRESEARCHANDMEDICALAPPLICATIONSTHEREHASBEENEXTENSIVERESEARCHONCOCLUSTERINGOFGENEEXPRESSIONDATAGENERATEDUSINGCDNAMICROARRAYSCOCLUSTERINGAPPROACHISANIMPORTANTANALYSISTOOLINGENEEXPRESSIONMEASUREMENT,WHENSOMEGENESHAVEMULTIPLEFUNCTIONSANDEXPERIMENTALCONDITIONSAREDIVERSEINTHISPAPER,WEINTRODUCEANEWFRAMEWORKFORMICROARRAYGENEEXPRESSIONDATACOCLUSTERINGTHEBASISOFTHISFRAMEWORKISABIPARTITEGRAPHREPRESENTATIONOF2DIMENSIONALGENEEXPRESSIONDATAWEHAVECONSTRUCTEDTHISBIPARTITEGRAPHBYPARTITIONINGTHESAMPLESETINTOTWODISJOINTSETSTHEKEYPROPERTYOFTHISREPRESENTATIONISTHAT,FORAGENESAMPLEMATRIX,ITCONSTRUCTSTHERANGEBIPARTITEGRAPH,ACOMPACTREPRESENTATIONOFALLSIMILARVALUERANGESBETWEENSAMPLECOLUMNSINORDERTOPRODUCETHESETOFCOCLUSTERS,ITSEARCHESFORCONSTRAINEDMAXIMALCLIQUESINTHISBIPARTITEGRAPHOURMETHODISSCALABLETOPRACTICALGENEEXPRESSIONDATAANDCANFINDSOMEINTERESTINGCOCLUSTERSINREALMICROARRAYDATASETSTHATMEETSPECIFICINPUTCONDITIONSKEYWORDSMICROARRAY;COCLUSTERING;GENEEXPRESSIONDATA;BIPARTITEGRAPHIINTRODUCTIONCLUSTERINGISANUNSUPERVISEDLEARNINGTECHNIQUE1WHICHISUSEDFORGROUPINGASETOFOBJECTSINTOSUBSETS,ORCLUSTERS,SUCHTHATTHOSEWITHINEACHCLUSTERAREMORECLOSELYRELATEDTOONEANOTHERTHANOBJECTSASSIGNEDTODIFFERENTCLUSTERSITISONEOFTHEMOSTCOMMONLYPERFORMEDANALYSESONGENEEXPRESSIONDATAGENEEXPRESSIONDATAAREASETOFMEASUREMENTSACCUMULATEDVIATHECDNAMICROARRAYORTHEOLIGONUCLEOTIDECHIPEXPERIMENTINGENEEXPRESSIONANALYSIS,THEAPPROACHOFCLUSTERINGGROUPSTHEGENESINTOBIOLOGICALLYRELEVANTCLUSTERSWITHSIMILAREXPRESSIONPATTERNSSOTHATTHEGENESTHATARECLUSTEREDTOGETHERTENDTOBEFUNCTIONALLYRELATEDSTANDARDCLUSTERINGTECHNIQUESCONSIDERTHEVALUEOFEACHPOINTINALLDIMENSIONS,INORDERTOFORMGROUPOFSIMILARPOINTSTHISTYPEOFONEWAYCLUSTERINGTECHNIQUES2,AREBASEDONSIMILARITYBETWEENSUBJECTSACROSSALLVARIABLESHOWEVERGENESMAYBECOREGULATEDUNDERLIMITEDCONDITIONSANDSHOWLITTLESIMILARITYOUTSIDETHESECONDITIONSCOCLUSTERING3,ISTRADITIONALLYAPPLIEDTOAMATRIXOFDATAVALUES,WHERETHEROWSAREDATAPOINTSANDTHECOLUMNSAREFEATURES,EGINMICROARRAYDATA,THEROWSAREGENESANDTHECOLUMNSAREEXPERIMENTEACHELEMENTOFTHISMATRIXREPRESENTSTHEEXPRESSIONLEVEL4OFAGENEUNDERASPECIFICCONDITION,ANDISREPRESENTEDBYAREALNUMBER,WHICHISUSUALLYTHELOGARITHMOFTHERELATIVEABUNDANCEOFTHEMRNAOFTHEGENEUNDERSPECIFICCONDITIONUNLIKECLUSTERINGWHICHSEEKSSIMILARROWSORCOLUMNS,COCLUSTERING,ALSOCALLEDBICLUSTERING,SEEKS“BLOCKS”OFROWSANDCOLUMNSTHATAREINTERRELATEDCOCLUSTERINGHASBEENPROVEDTOBEOFGREATVALUEFORFINDINGTHEINTERESTINGPATTERNSINTHEMICROARRAYEXPRESSIONDATA,WHICHRECORDSTHEEXPRESSIONLEVELSOFMANYGENES,FORDIFFERENTBIOLOGICALSAMPLESMOREOVER,COCLUSTERINGCANIDENTIFYOVERLAPPINGPATTERNSANDHENCELEADSTOTHEPOSSIBILITYTHATAGENEMAYBEAMEMBEROFMULTIPLEPATHWAYS5ITISANAPPROACHTHATFINDSLOCALPATTERNWHEREASUBSETOFOBJECTSMIGHTBESIMILARTOEACHOTHERBASEDONONLYASUBSETOFATTRIBUTESIIRELATEDWORKCOCLUSTERING,ORBICLUSTERING,ISANINTERESTINGPARADIGMFORUNSUPERVISEDDATAANALYSISASITISMOREINFORMATIVE,HASLESSPARAMETERS,ISSCALABLEANDISABLETOEFFECTIVELYINTERWINEROWANDCOLUMNINFORMATIONSEVERALAPPROACHESHAVEBEENPROPOSEDFORSOLVINGCOCLUSTERINGPROBLEMBUTWECONCENTRATEONGRAPHBASEDCLUSTERING2,5,6,7,10APPROACHESASITISKNOWNTOBENPHARDPROBLEM,SEVERALALGORITHMSFORMININGCOCLUSTERSUSEHEURISTICMETHODSORPROBABILISTICAPPROXIMATION,WHICHDECREASESTHEACCURACYOFFINALCLUSTERINGRESULTSANILLUSTRATIVEDISCUSSIONONMANYOFTHESEALGORITHMSCANBEFOUNDIN8,9THEREAREFOURMAJORCLASSESOFCOCLUSTERICOCLUSTERWITHCONSTANTVALUESIICOCLUSTERWITHCONSTANTVALUESONROWSORCOLUMNSIIICOCLUSTERWITHCOHERENTVALUESIVCOCLUSTERWITHCOHERENTEVOLUTIONALARGENUMBEROFSUCHALGORITHMSASSUMEEITHERADDITIVEORMULTIPLICATIVEMODELSTHEBICLUSTERDEFINEDBYCHENGCHURCH3ISASUBSETOFROWSANDSUBSETOFCOLUMNSWITHAHIGHSIMILARITYSCORETHISSIMILARITYSCOREIS9781424447138/10/25002010IEEECALLEDMEANSQUAREDRESIDUE,H,WASUSEDASAMEASUREOFTHECOHERENCEOFTHEROWSANDCOLUMNSINTHEBICLUSTERASUBMATRIX,JIISCONSIDEREDAΔBICLUSTERIFΔ,JIHFORSOME0≥ΔINORDERTOASSESSTHEOVERALLQUALITYOFAΔBICLUSTER,CHENGCHURCHDEFINEDTHEMEANSQUAREDRESIDUE,H,OFABICLUSTER,JIASTHESUMOFTHESQUAREDRESIDUES∑∈∈JJIIIJARJIJIH,21,WHERERAIJAIJAIJAIJAIJ,AIJ,AIJANDAIJREPRESENTROWMEAN,COLUMNMEANANDBICLUSTERMEANRESPECTIVELYHERETHEYASSUMETHATTHEREARENOMISSINGVALUESINTHEDATAMATRIXANDHENCETHEYREPLACETHEMISSINGVALUESBYRANDOMNUMBERS,DURINGAPREPROCESSINGPHASETANAYETAL7MODELEDTHEDATAMATRIXASABIGRAPHANDUSEDSTATISTICALMODELSTOSOLVETHEPROBLEMINORDERTOIDENTIFYBICLIQUESTHEYHAVEUSEDAMERITFUNCTIONTOEVALUATETHEQUALITYOFACOMPUTEDBICLUSTERAHSANETAL2PROPOSEDAGRAPHDRAWINGBASEDBICLUSTERINGTECHNIQUEUSINGTHECROSSINGMINIMIZATIONPARADIGMTHATEMPLOYSASTATICDISCRETIZATIONOFTHEINPUTDATAMATRIXAHMADETAL5PROPOSEDAGRAPHDRAWINGBASEDBICLUSTERINGTECHNIQUEUSINGSPECTRALPARTITIONINGBASEDONCROSSINGMINIMIZATIONPARADIGMTHEYSHOWEDTHATMINIMIZATIONOFHALL’SENERGYFUNCTIONCORRESPONDSTOFINDINGTHENORMALIZEDCUTOFTHEBIGRAPHIIIBASICCONCEPTSAGENEEXPRESSIONDATASETCANBEREPRESENTEDBYAREALVALUEDEXPRESSIONMATRIX⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎣⎡NDNNDDXXXXXXXXXD212222111211WHERENISTHENUMBEROFGENES,DISTHENUMBEROFEXPERIMENTALCONDITIONSORSAMPLESANDIJXISTHEMEASUREDEXPRESSIONLEVELOFGENEIINSAMPLEJLETUSCONSIDER},,,{110−NGGGGBEASETOFNGENESAND},,{110−MSSSSBEASETOFMBIOLOGICALSAMPLESAD−2MICROARRAYDATASETISAREALVALUEDMNMATRIX}{IJDSGDWHERE1,0−∈NI,1,0−∈MJLETBBEASUBMATRIXOFDATASETDCOCLUSTER}{IJBYXBWHEREGX⊆ANDSY⊆,PROVIDEDCERTAINCONDITIONSOFHOMOGENEITYARESATISFIEDLET⎥⎦⎤⎢⎣⎡JQIQJPIPBBBBB2,2BEANYARBITRARYSUBMATRIXOFBTHENBISASCALINGCLUSTERIFIPIIQBBΑANDJPJJQBBΑ;ANDΡΑΑ≤−JI,WHEREΑISACONSTANTMULTIPLICATIVEFACTORBISASHIFTINGCLUSTERIFFIPIIQBBΒANDJPJJQBBΒ;ANDΡΒΒ≤−JI,WHEREΒISCONSTANTADDITIVEFACTORWESAYTHATTHECLUSTERYXBISASUBSETOFYXB,IFFXX⊆ANDYY⊆LETSBETHESETOFALLCOCLUSTERSTHATSATISFYTHEGIVENHOMOGENEITYCONDITIONS,THENSB∈ISCALLEDAMAXIMALCOCLUSTERIFFTHEREDOESN’TEXISTANOTHERCLUSTERSB∈SUCHTHATBB⊂WECALLBISAVALIDCLUSTERIFFITISAMAXIMALCOCLUSTERSATISFYINGTHEFOLLOWINGCONDITIONSALETUSCONSIDERMMIIJIBGM11⎭⎬⎫⎩⎨⎧∏BETHEGEOMETRICMEANBETWEENTWOSPECIFIEDCOLUMNVALUESFORAGIVENROWAND∑IIIGMGMWBETHEWEIGHTOFTHEROWFORTHISSPECIFIEDTWOCOLUMNVALUESBLETUSCONSIDERIPIQIIBBWR−ANDJQIQJJBBWR−BETHEWEIGHTEDDIFFERENCEOFTWOCOLUMNVALUESFORAGIVENROWIORJWENEEDTHATΡ≤−,MIN,MAXJIJIRRRR;WHEREΡISAWEIGHTINTHECORRESPONDINGGENESETCWENEEDTHATXXΣ≥|ANDYYΣ≥,WHEREXΣANDYΣDENOTEMINIMUMCARDINALITYTHRESHOLDSFOREACHDIMENSIONINORDERTOMINELARGEENOUGHCLUSTERS,THEMINIMUMSIZECONSTRAINTSIEXΣ,ANDYΣAREIMPOSEDDEFINITION31BIPARTITEGRAPHAGRAPH,EVGISCALLEDBIPARTITEIFITSVERTEXSETVCANBEDECOMPOSEDINTOTWODISJOINTSUBSETS1VAND2VIE21VVV∪SUCHTHATEVERYEDGEINGJOINSAVERTEXIN1VWITHAVERTEXIN2VIEΦ∩21VVWECONSIDERWEIGHTEDBIPARTITEGRAPH,,,21WEVVGWITHIJWWWHERE0≥IJWDENOTESTHEWEIGHTOFTHEEDGE},{JIBETWEENVERTICESIANDJIVTHECOCLUSTERALGORITHMFROMTHEDATAMATRIX,THECOCLUSTERINGALGORITHMMINESARBITRARILYPOSITIONEDANDOVERLAPPING,SCALINGANDSHIFTINGPATTERNSTHISALGORITHMHASTWOSTEPSIFORSGMATRIX,FINDTHEVALIDWEIGHTEDDIFFERENCERANGESFORALLPAIROFSAMPLESANDCONSTRUCTARANGEBIPARTITEGRAPHIICOCLUSTERSIDENTIFICATIONFROMTHEWEIGHTEDRANGEBIPARTITEGRAPHACONSTRUCTINGRANGEBIPARTITEGRAPHFORAGIVENDATASETD,THEMINIMUMSIZETHRESHOLD,XΣANDYΣ,ANDTHEMAXIMUMWEIGHTEDDIFFERENCETHRESHOLDΡ,LETUSANDVSBEANYTWOSAMPLECOLUMNSOFDANDLETXVXUXUVXDDWR−BETHEWEIGHTEDDIFFERENCEOFTHEEXPRESSIONVALUESOFGENEXGINCOLUMNSUSANDVSSUCHTHATVU,WHERE1,0−∈NXINORDERTOINCORPORATETHEIDEAOFMUTUALIMPORTANCEBETWEENTWOCOLUMNS,WEHAVECOMPUTEDTHEWEIGHTOFALLROWSFORSPECIFIEDCOLUMNSADIFFERENCERANGEISDEFINEDASANINTERVALOFDIFFERENCEVALUES,1HRR,WITHHRR1LET},{,1HUVXXHLRRRGRRJ∈BETHESETOFGENES,WHOSEDIFFERENCEWRTCOLUMNSUSANDVSLIEINTHEGIVENWEIGHTEDDIFFERENCERANGEADIFFERENCERANGEISCALLEDVALIDIFFΡ≤−,MIN,MAX11RRRRHH,WHEREΡISTHEROWWEIGHTINTHEVALIDRANGENORMALLY,FORMICROARRAYEXPERIMENTDATA,GENESANDSAMPLESAREREPRESENTEDBY1VAND2VVERTEXSETSRESPECTIVELY,ANDTHEEDGEWEIGHTIJWREPRESENTSTHERESPONSEOFI’THGENETOJ’THSAMPLEHOWEVER,INORDERTOHAVEAVERYCOMPACTREPRESENTATION,INTHISPAPER,WECONSTRUCTTHEWEIGHTEDUNDIRECTEDBIPARTITEGRAPHBYPARTITIONINGTHESAMPLESETINTOTWODISJOINTSETSCALLEDUPPERLAYER1VANDLOWERLAYER2VTHESAMPLESTHATDONOTHAVEANYDATAVALUESARENOTCONSIDEREDINTHEFORMATIONOFDISJOINTSETSHERE,EACHEDGEINTHERANGEBIPARTITEGRAPHHASASSOCIATEDWITHITTHEWEIGHTANDGENESETCORRESPONDINGTOTHERANGEONTHATEDGEDIFFERENTBIPARTITEGRAPHSEMERGEDFORDIFFERENTTHRESHOLDVALUE,WHICHISANYWEIGHTVALUEINTHECORRESPONDINGGENESETCONSEQUENTLY,WEWILLHAVEDIFFERENTTYPESOFCOCLUSTERSINORDERTOINCLUDEEDGESWITHLARGEGENESET,WEHAVEASSIGNEDRANKTOVALIDEDGES,WHICHAREDEFINEDBELOW⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧≥1|,|2|,|12HLHLRRJOUNTFREQUENCYCANDSRRJIFOTHERWISEEDGERANKTHEINCLUSIONANDDELETIONOFEDGESDEPENDSUPONTHEVALUEOFTHISRANKEDGEANDORDERINWHICHWEPROCESSTHESESAMPLESWECOMPUTEFREQUENCYCOUNTFOREACHEDGE,WHICHISTHEOCCURRENCEOFCARDINALITYOFGENESETTABLE1EXAMPLEOFMICROARRAYDATASETS0S1S2S3S4S5S6G0361010101010G130252010G2505050G3665520G490756030G5664420G6303030G780808080G860504020G94040404040FIGURE1SHOWSTHEWEIGHTEDDIFFERENCEVALUESFORDIFFERENTGENESUSINGCOLUMNSS4ANDS6,FORTABLE1HERETHEVALUEOF040Ρ,WHICHISTHEMINIMUMROWWEIGHTINTHEGENESET,ANDCONSIDERING3XΣ,YΣ2,THENTHEREISONLYONEVALIDWEIGHTEDDIFFERENCERANGE00,00ANDTHECORRESPONDINGGENESETIS},,,{00,009620,64GGGGJSSINTHISCASE,THENUMBEROFVALIDRANGESDEPENDSONTHEVALUEOFΡFORTHESORTEDDIFFERENCEVALUES,THISALGORITHMFINDALLVALIDWEIGHTEDDIFFERENCERANGESFORALLPAIROFCOLUMNSSSSVU∈,HEREWEMAYHAVEOVERLAPPINGOFDIFFERENTRANGESTHEALGORITHMFORPARTITIONINGVERTEXSETINTO1VAND2V,FORCONSTRUCTIONOFBIPARTITEGRAPHISGIVENINFIGURE2FROMTABLE1,WEHAVECONSTRUCTEDAMAXIMALWEIGHTEDRANGEBIPARTITEGRAPHFIGURE3LETS′BETHESETOFCOLUMNSWITHMISSINGVALUEINEACHROWWEHAVETAKENWEIGHTOFTHEEDGEASMAXIMUMWEIGHTINTHECORRESPONDINGGENESETTHISALGORITHMGIVESEMPHASISTOTHEEDGESHAVINGLARGEGENESETINORDERTOCOMPENSATETHEDELETIONOFFEWVALIDEDGES,WHILEPARTITIONINGTHESAMPLESETINTOTWODISJOINTSETSASWEDEALWITHNOISYDATA,ADDITIVEANDMULTIPLICATIVEMETHODSOFFINDINGCLUSTERSMAYNOTALWAYSLEADTOGOODRESULTSTHEREFORE,INSTEADOFCOMPARINGTWOCOLUMNVALUESINDEPENDENTLY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