七年级下《压强》教学下载浙教版

Chapter20:DataAnalysis........Chapter20:DataAnalysis...Chapter20:DataAnalysisDecisionSupportSystemsDataWarehousingDataMiningClassificationAssociationRulesClustering........Chapter20:DataAnalysisDeciDecisionSupportSystemsDecision-supportsystemsareusedtomakebusinessdecisions,oftenbasedondatacollectedbyon-linetransaction-processingsystems.Examplesofbusinessdecisions:Whatitemstostock?Whatinsurancepremiumtochange?Towhomtosendadvertisements?Examplesofdatausedformakingdecisions Retailsalestransactiondetails Customerprofiles(income,age,gender,etc.)........DecisionSupportSystemsDecisiDecision-SupportSystems:OverviewDataanalysistasksaresimplifiedbyspecializedtoolsandSQLextensionsExampletasksForeachproductcategoryandeachregion,whatwerethetotalsalesinthelastquarterandhowdotheycomparewiththesamequarterlastyearAsabove,foreachproductcategoryandeachcustomercategoryStatisticalanalysispackages(e.g.,:S++)canbeinterfacedwithdatabasesStatisticalanalysisisalargefield,butnotcoveredhereDataminingseekstodiscoverknowledgeautomaticallyintheformofstatisticalrulesandpatternsfromlargedatabases.Adatawarehousearchivesinformationgatheredfrommultiplesources,andstoresitunderaunifiedschema,atasinglesite.Importantforlargebusinessesthatgeneratedatafrommultipledivisions,possiblyatmultiplesitesDatamayalsobepurchasedexternally........Decision-SupportSystems:OverDataWarehousingDatasourcesoftenstoreonlycurrentdata,nothistoricaldataCorporatedecisionmakingrequiresaunifiedviewofallorganizationaldata,includinghistoricaldataAdatawarehouseisarepository(archive)ofinformationgatheredfrommultiplesources,storedunderaunifiedschema,atasinglesiteGreatlysimplifiesquerying,permitsstudyofhistoricaltrendsShiftsdecisionsupportqueryloadawayfromtransactionprocessingsystems........DataWarehousingDatasourcesoDataWarehousing........DataWarehousing...DesignIssuesWhenandhowtogatherdataSourcedrivenarchitecture:datasourcestransmitnewinformationtowarehouse,eithercontinuouslyorperiodically(e.g.,atnight)Destinationdrivenarchitecture:warehouseperiodicallyrequestsnewinformationfromdatasourcesKeepingwarehouseexactlysynchronizedwithdatasources(e.g.,usingtwo-phasecommit)istooexpensiveUsuallyOKtohaveslightlyout-of-datedataatwarehouseData/updatesareperiodicallydownloadedformonlinetransactionprocessing(OLTP)systems.WhatschematouseSchemaintegration........DesignIssuesWhenandhowtogMoreWarehouseDesignIssuesDatacleansingE.g.,correctmistakesinaddresses(misspellings,zipcodeerrors)MergeaddresslistsfromdifferentsourcesandpurgeduplicatesHowtopropagateupdatesWarehouseschemamaybea(materialized)viewofschemafromdatasourcesWhatdatatosummarizeRawdatamaybetoolargetostoreon-lineAggregatevalues(totals/subtotals)oftensufficeQueriesonrawdatacanoftenbetransformedbyqueryoptimizertouseaggregatevalues........MoreWarehouseDesignIssuesDaWarehouseSchemasDimensionvaluesareusuallyencodedusingsmallintegersandmappedtofullvaluesviadimensiontablesResultantschemaiscalledastarschemaMorecomplicatedschemastructuresSnowflakeschema:multiplelevelsofdimensiontablesConstellation:multiplefacttables........WarehouseSchemasDimensionvalDataWarehouseSchema........DataWarehouseSchema...DataMiningDataminingistheprocessofsemi-automaticallyanalyzinglargedatabasestofindusefulpatterns

PredictionbasedonpasthistoryPredictifacreditcardapplicantposesagoodcreditrisk,basedonsomeattributes(income,jobtype,age,..)andpasthistoryPredictifapatternofphonecallingcardusageislikelytobefraudulentSomeexamplesofpredictionmechanisms:ClassificationGivenanewitemwhoseclassisunknown,predicttowhichclassitbelongsRegressionformulaeGivenasetofmappingsforanunknownfunction,predictthefunctionresultforanewparametervalue........DataMiningDataminingistheDataMining(Cont.)DescriptivePatternsAssociationsFindbooksthatareoftenboughtby“similar”customers.Ifanewsuchcustomerbuysonesuchbook,suggesttheotherstoo.AssociationsmaybeusedasafirststepindetectingcausationE.g.,associationbetweenexposuretochemicalXandcancer,ClustersE.g.,typhoidcaseswereclusteredinanareasurroundingacontaminatedwellDetectionofclustersremainsimportantindetectingepidemics........DataMining(Cont.)DescriptiveClassificationRulesClassificationruleshelpassignnewobjectstoclasses.E.g.,givenanewautomobileinsuranceapplicant,shouldheorshebeclassifiedaslowrisk,mediumriskorhighrisk?Classificationrulesforaboveexamplecoulduseavarietyofdata,suchaseducationallevel,salary,age,etc.

personP,P.degree=mastersandP.income>75,000

P.credit=excellent

personP,P.degree=bachelorsand

(P.income

25,000andP.income

75,000)

P.credit=goodRulesarenotnecessarilyexact:theremaybesomemisclassificationsClassificationrulescanbeshowncompactlyasadecisiontree.........ClassificationRulesClassificaDecisionTree........DecisionTree...ConstructionofDecisionTreesTrainingset:adatasampleinwhichtheclassificationisalreadyknown.

Greedytopdowngenerationofdecisiontrees.Eachinternalnodeofthetreepartitionsthedataintogroupsbasedonapartitioningattribute,andapartitioningcondition

forthenodeLeafnode:all(ormost)oftheitemsatthenodebelongtothesameclass,orallattributeshavebeenconsidered,andnofurtherpartitioningispossible.........ConstructionofDecisionTreesBestSplitsPickbestattributesandconditionsonwhichtopartitionThepurityofasetSoftraininginstancescanbemeasuredquantitativelyinseveralways.Notation:numberofclasses=k,numberofinstances=|S|,

fractionofinstancesinclassi=pi.TheGinimeasureofpurityisdefinedas[ Gini(S)=1-

Whenallinstancesareinasingleclass,theGinivalueis0Itreachesitsmaximum(of1–1/k)ifeachclassthesamenumberofinstances.

ki-1p2i........BestSplitsPickbestattributeBestSplits(Cont.)Anothermeasureofpurityistheentropy

measure,whichisdefinedas entropy(S)=–

WhenasetSissplitintomultiplesetsSi,I=1,2,…,r,wecanmeasurethepurityoftheresultantsetofsetsas:

purity(S1,S2,…..,Sr)=

TheinformationgainduetoparticularsplitofSintoSi,i=1,2,….,r

Information-gain(S,{S1,S2,….,Sr)=purity(S)–purity(S1,S2,…Sr)

ri=1|Si||S|purity(Si)ki-1pilog2pi........BestSplits(Cont.)AnothermeaBestSplits(Cont.)Measureof“cost”ofasplit:

Information-content(S,{S1,S2,…..,Sr}))=–

Information-gainratio=Information-gain(S,{S1,S2,……,Sr}) Information-content(S,{S1,S2,…..,Sr})Thebestsplitistheonethatgivesthemaximuminformationgainratiolog2ri-1|Si||S||Si||S|

........BestSplits(Cont.)MeasureofFindingBestSplitsCategoricalattributes(withnomeaningfulorder):Multi-waysplit,onechildforeachvalueBinarysplit:tryallpossiblebreakupofvaluesintotwosets,andpickthebestContinuous-valuedattributes(canbesortedinameaningfulorder)Binarysplit:Sortvalues,tryeachasasplitpointE.g.,ifvaluesare1,10,15,25,splitat1,10,15PickthevaluethatgivesbestsplitMulti-waysplit:Aseriesofbinarysplitsonthesameattributehasroughlyequivalenteffect........FindingBestSplitsCategoricalDecision-TreeConstructionAlgorithm

ProcedureGrowTree(S)

Partition(S);

ProcedurePartition(S)

if(purity(S)>

por|S|<s)then

return;

foreachattributeA

evaluatesplitsonattributeA;

Usebestsplitfound(acrossallattributes)topartition

SintoS1,S2,….,Sr,

fori=1,2,…..,r

Partition(Si);........Decision-TreeConstructionAlgOtherTypesofClassifiersNeuralnetclassifiersarestudiedinartificialintelligenceandarenotcoveredhereBayesianclassifiersuseBayestheorem,whichsays

p(cj|d)=p(d|cj)p(cj)

p(d)

where

p(cj|d)=probabilityofinstancedbeinginclasscj,

p(d|cj)=probabilityofgeneratinginstancedgivenclasscj,

p(cj

)

=probabilityofoccurrenceofclasscj,and

p(d)=probabilityofinstancedoccuring

........OtherTypesofClassifiersNeurNaïveBayesianClassifiersBayesianclassifiersrequirecomputationofp(d|cj)precomputationofp(cj)

p(d)canbeignoredsinceitisthesameforallclassesTosimplifythetask,naïveBayesianclassifiersassumeattributeshaveindependentdistributions,andtherebyestimate

p(d|cj)=p(d1|cj)*p(d2|cj)*….*(p(dn|cj)Eachofthep(di|cj)canbeestimatedfromahistogramondivaluesforeachclasscjthehistogramiscomputedfromthetraininginstancesHistogramsonmultipleattributesaremoreexpensivetocomputeandstore........NaïveBayesianClassifiersBayeRegressionRegressiondealswiththepredictionofavalue,ratherthanaclass.Givenvaluesforasetofvariables,X1,X2,…,Xn,wewishtopredictthevalueofavariableY.Onewayistoinfercoefficientsa0,a1,a1,…,ansuchthat

Y=a0+a1*X1+a2*X2+…+an*Xn

Findingsuchalinearpolynomialiscalledlinearregression.Ingeneral,theprocessoffindingacurvethatfitsthedataisalsocalledcurvefitting.Thefitmayonlybeapproximatebecauseofnoiseinthedata,orbecausetherelationshipisnotexactlyapolynomialRegressionaimstofindcoefficientsthatgivethebestpossiblefit.........RegressionRegressiondealswitAssociationRulesRetailshopsareofteninterestedinassociationsbetweendifferentitemsthatpeoplebuy.SomeonewhobuysbreadisquitelikelyalsotobuymilkApersonwhoboughtthebookDatabaseSystemConceptsisquitelikelyalsotobuythebookOperatingSystemConcepts.Associationsinformationcanbeusedinseveralways.E.g.,whenacustomerbuysaparticularbook,anonlineshopmaysuggestassociatedbooks.Associationrules:

bread

milkDB-Concepts,OS-ConceptsNetworksLefthandside:antecedent,righthandside:consequentAnassociationrulemusthaveanassociatedpopulation;thepopulationconsistsofasetofinstancesE.g.,eachtransaction(sale)atashopisaninstance,andthesetofalltransactionsisthepopulation........AssociationRulesRetailshopsAssociationRules(Cont.)Ruleshaveanassociatedsupport,aswellasanassociatedconfidence.Support

isameasureofwhatfractionofthepopulationsatisfiesboththeantecedentandtheconsequentoftherule.E.g.,supposeonly0.001percentofallpurchasesincludemilkandscrewdrivers.Thesupportfortheruleismilk

screwdriversislow.Confidence

isameasureofhowoftentheconsequentistruewhentheantecedentistrue.E.g.,therulebread

milkhasaconfidenceof80percentif80percentofthepurchasesthatincludebreadalsoincludemilk.........AssociationRules(Cont.)RulesFindingAssociationRulesWearegenerallyonlyinterestedinassociationruleswithreasonablyhighsupport(e.g.,supportof2%orgreater)NaïvealgorithmConsiderallpossiblesetsofrelevantitems.Foreachsetfinditssupport(i.e.,counthowmanytransactionspurchaseallitemsintheset).Largeitemsets:setswithsufficientlyhighsupportUselargeitemsetstogenerateassociationrules.FromitemsetAgeneratetheruleA-{b}bforeachb

A.Supportofrule=support(A).Confidenceofrule=support(A)/support(A-{b})........FindingAssociationRulesWearFindingSupportDeterminesupportofitemsetsviaasinglepassonsetoftransactionsLargeitemsets:setswithahighcountattheendofthepassIfmemorynotenoughtoholdallcountsforallitemsetsusemultiplepasses,consideringonlysomeitemsetsineachpass.Optimization:Onceanitemsetiseliminatedbecauseitscount(support)istoosmallnoneofitssupersetsneedstobeconsidered.Theaprioritechniquetofindlargeitemsets:Pass1:countsupportofallsetswithjust1item.EliminatethoseitemswithlowsupportPassi:candidates:everysetofiitemssuchthatallitsi-1itemsubsetsarelargeCountsupportofallcandidatesStopiftherearenocandidates........FindingSupportDeterminesuppoOtherTypesofAssociationsBasicassociationruleshaveseverallimitationsDeviationsfromtheexpectedprobabilityaremoreinterestingE.g.,ifmanypeoplepurchasebread,andmanypeoplepurchasecereal,quiteafewwouldbeexpectedtopurchasebothWeareinterestedinpositiveaswellasnegativecorrelationsbetweensetsofitemsPositivecorrelation:co-occurrenceishigherthanpredictedNegativecorrelation:co-occurrenceislowerthanpredictedSequenceassociations/correlationsE.g.,wheneverbondsgoup,stockpricesgodownin2daysDeviationsfromtemporalpatternsE.g.,deviationfromasteadygrowthE.g.,salesofwinterweargodowninsummerNotsurprising,partofaknownpattern.Lookfordeviationfromvaluepredictedusingpastpatterns........OtherTypesofAssociationsBasClusteringClustering:Intuitively,findingclustersofpointsinthegivendatasuchthatsimilarpointslieinthesameclusterCanbeformalizedusingdistancemetricsinseveralwaysGrouppointsintoksets(foragivenk)suchthattheaveragedistanceofpointsfromthecentroidoftheirassignedgroupisminimizedCentroid:pointdefinedbytakingaverageofcoordinatesineachdimension.Anothermetric:minimizeaveragedistancebetweeneverypairofpointsinaclusterHasbeenstudiedextensivelyinstatistics,butonsmalldatasetsDataminingsystemsaimatclusteringtechniquesthatcanhandleverylargedatasetsE.g.,theBirchclusteringalgorithm(moreshortly)........ClusteringClustering:IntuitivHierarchicalClusteringExamplefrombiologicalclassification(thewordclassificationheredoesnotmeanapredictionmechanism)chordata

mammaliareptilia

leopardshumanssnakescrocodilesOtherexamples:Internetdirectorysystems(e.g.,Yahoo,moreonthislater)AgglomerativeclusteringalgorithmsBuildsmallclusters,thenclustersmallclustersintobiggerclusters,andsoonDivisiveclusteringalgorithmsStartwithallitemsinasinglecluster,repeatedlyrefine(break)clustersintosmallerones........HierarchicalClusteringExampleClusteringAlgorithmsClusteringalgorithmshavebeendesignedtohandleverylargedatasetsE.g.,theBirchalgorithmMainidea:useanin-memoryR-treetostorepointsthatarebeingclusteredInsertpointsoneatatimeintotheR-tree,merginganewpointwithanexistingclusterifislessthansome

distanceawayIftherearemoreleafnodesthanfitinmemory,mergeexistingclustersthatareclosetoeachotherAttheendoffirstpasswegetalargenumberofclustersattheleavesoftheR-treeMergeclusterstoreducethenumberofclusters........Clu