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1MiningFrequentPatterns,AssociationandCorrelations:BasicConceptsandMethodsBasicConceptsFrequentItemsetMiningMethodsWhichPatternsAreInteresting?—PatternEvaluationMethodsSummary2WhatIsFrequentPatternAnalysis?Frequentpattern:apattern(asetofitems,subsequences,substructures,etc.)thatoccursfrequentlyinadatasetFirstproposedbyAgrawal,Imielinski,andSwami[AIS93]inthecontextoffrequentitemsetsandassociationruleminingMotivation:FindinginherentregularitiesindataWhatproductswereoftenpurchasedtogether?—Beeranddiapers?!WhatarethesubsequentpurchasesafterbuyingaPC?WhatkindsofDNAaresensitivetothisnewdrug?Canweautomaticallyclassifywebdocuments?ApplicationsBasketdataanalysis,cross-marketing,catalogdesign,salecampaignanalysis,Weblog(clickstream)analysis,andDNAsequenceanalysis.3WhyIsFreq.PatternMiningImportant?Freq.pattern:AnintrinsicandimportantpropertyofdatasetsFoundationformanyessentialdataminingtasksAssociation,correlation,andcausalityanalysisSequential,structural(e.g.,sub-graph)patternsPatternanalysisinspatiotemporal,multimedia,time-series,andstreamdataClassification:discriminative,frequentpatternanalysisClusteranalysis:frequentpattern-basedclusteringDatawarehousing:icebergcubeandcube-gradientSemanticdatacompression:fasciclesBroadapplications4BasicConcepts:FrequentPatternsitemset:Asetofoneormoreitemsk-itemsetX={x1,…,xk}(absolute)support,or,supportcountofX:FrequencyoroccurrenceofanitemsetX(relative)
support,s,isthefractionoftransactionsthatcontainsX(i.e.,theprobabilitythatatransactioncontainsX)AnitemsetXisfrequentifX’ssupportisnolessthanaminsupthresholdCustomerbuysdiaperCustomerbuysbothCustomerbuysbeerTidItemsbought10Beer,Nuts,Diaper20Beer,Coffee,Diaper30Beer,Diaper,Eggs40Nuts,Eggs,Milk50Nuts,Coffee,Diaper,Eggs,Milk5BasicConcepts:AssociationRulesFindalltherulesXY
withminimumsupportandconfidencesupport,s,probabilitythatatransactioncontainsXYconfidence,c,
conditionalprobabilitythatatransactionhavingXalsocontainsYLetminsup=50%,minconf=50%Freq.Pat.:Beer:3,Nuts:3,Diaper:4,Eggs:3,{Beer,Diaper}:3CustomerbuysdiaperCustomerbuysbothCustomerbuysbeerNuts,Eggs,Milk40Nuts,Coffee,Diaper,Eggs,Milk50Beer,Diaper,Eggs30Beer,Coffee,Diaper20Beer,Nuts,Diaper10ItemsboughtTidAssociationrules:(manymore!)BeerDiaper(60%,100%)DiaperBeer(60%,75%)6ClosedPatternsandMax-PatternsAlongpatterncontainsacombinatorialnumberofsub-patterns,e.g.,{a1,…,a100}contains(1001)+(1002)+…+(110000)=2100–1=1.27*1030sub-patterns!Solution:Mineclosedpatternsandmax-patternsinsteadAnitemsetX
isclosedifXisfrequentandthereexistsnosuper-patternY?X,withthesamesupportasX(proposedbyPasquier,etal.@ICDT’99)AnitemsetXisamax-patternifXisfrequentandthereexistsnofrequentsuper-patternY?X(proposedbyBayardo@SIGMOD’98)Closedpatternisalosslesscompressionoffreq.patternsReducingthe#ofpatternsandrules7ClosedPatternsandMax-PatternsExercise.DB={<a1,…,a100>,<a1,…,a50>}Min_sup=1.Whatisthesetofcloseditemset?<a1,…,a100>:1<a1,…,a50>:2Whatisthesetofmax-pattern?<a1,…,a100>:1Whatisthesetofallpatterns?!!8ComputationalComplexityofFrequentItemsetMiningHowmanyitemsetsarepotentiallytobegeneratedintheworstcase?ThenumberoffrequentitemsetstobegeneratedissenstivetotheminsupthresholdWhenminsupislow,thereexistpotentiallyanexponentialnumberoffrequentitemsetsTheworstcase:MNwhereM:#distinctitems,andN:maxlengthoftransactionsTheworstcasecomplextyvs.theexpectedprobabilityEx.SupposeWalmarthas104kindsofproductsThechancetopickuponeproduct10-4Thechancetopickupaparticularsetof10products:~10-40Whatisthechancethisparticularsetof10productstobefrequent103timesin109transactions?9Chapter5:MiningFrequentPatterns,AssociationandCorrelations:BasicConceptsandMethodsBasicConceptsFrequentItemsetMiningMethodsWhichPatternsAreInteresting?—PatternEvaluationMethodsSummary10ScalableFrequentItemsetMiningMethodsApriori:ACandidateGeneration-and-TestApproachImprovingtheEfficiencyofAprioriFPGrowth:AFrequentPattern-GrowthApproachECLAT:FrequentPatternMiningwithVerticalDataFormat11TheDownwardClosurePropertyandScalableMiningMethodsThedownwardclosurepropertyoffrequentpatternsAnysubsetofafrequentitemsetmustbefrequentIf{beer,diaper,nuts}isfrequent,sois{beer,diaper}i.e.,everytransactionhaving{beer,diaper,nuts}alsocontains{beer,diaper}Scalableminingmethods:ThreemajorapproachesApriori(Agrawal&Srikant@VLDB’94)Freq.patterngrowth(FPgrowth—Han,Pei&Yin@SIGMOD’00)Verticaldataformatapproach(Charm—Zaki&Hsiao@SDM’02)12Apriori:ACandidateGeneration&TestApproachAprioripruningprinciple:Ifthereisanyitemsetwhichisinfrequent,itssupersetshouldnotbegenerated/tested!(Agrawal&Srikant@VLDB’94,Mannila,etal.@KDD’94)Method:Initially,scanDBoncetogetfrequent1-itemsetGeneratelength(k+1)candidateitemsetsfromlengthkfrequentitemsetsTestthecandidatesagainstDBTerminatewhennofrequentorcandidatesetcanbegenerated13TheAprioriAlgorithm—AnExampleDatabaseTDB1stscanC1L1L2C2C22ndscanC3L33rdscanTidItems10A,C,D20B,C,E30A,B,C,E40B,EItemsetsup{A}2{B}3{C}3{D}1{E}3Itemsetsup{A}2{B}3{C}3{E}3Itemset{A,B}{A,C}{A,E}{B,C}{B,E}{C,E}Itemsetsup{A,B}1{A,C}2{A,E}1{B,C}2{B,E}3{C,E}2Itemsetsup{A,C}2{B,C}2{B,E}3{C,E}2Itemset{B,C,E}Itemsetsup{B,C,E}2Supmin=214TheAprioriAlgorithm(Pseudo-Code)Ck:CandidateitemsetofsizekLk:frequentitemsetofsizekL1={frequentitems};for
(k=1;Lk!=;k++)dobegin
Ck+1=candidatesgeneratedfromLk;
foreachtransactiontindatabasedoincrementthecountofallcandidatesinCk+1thatarecontainedint
Lk+1=candidatesinCk+1withmin_support
endreturn
k
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