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EvolutionaryModelsandDynamicalPropertiesofComplexNetworksName:JianguoLiuUniversityofShanghaiforScienceandTechnology2010-3-241OutlineComplexnetworksanalysisbyCitespaceNetworkevolutionmodelsDynamicalpropertiesonscale-freenetworksPersonalizedrecommendation21999年-2010年发表的以“complexnetworks”为主题词的SCI论文数3Citespace软件介绍CiteSpace：由美国德雷赛尔大学信息科学与技术学院的陈超美开发。该程序可以登录到/~cchen/citespace后免费使用。利用Citespace寻找某一学科领域的研究进展和当前的研究前沿，及其对应的基础知识。

4复杂网络论文作者合作网(1999-2010)5复杂网络研究小组状况(1999-2010)6复杂网络各个国家研究状况(1999-2010)7利用引文分析观察当前的研究热点(1999-2010)8Topcitedauthors(1999-2010)9各研究领域之间的关系(1999-2010)10个性化化推荐荐的知知识图图谱11Topcitedauthors12目前的的研究究热点点13OutlineBackgroundintroductionNetworkevolutionmodelsDynamicalPersonalizedrecommendation142.Scale-freeNetworkEvolutionModelsMultistagerandomgrowingsmall-worldnetworkswithpower-lawdegreedistributionGrowingscale-freenetworkmodelwithtunableassortativecoefficientSelf-learningmutualselectionmodelforweightednetworksRandomevolvingnetworksunderthediameteranddverageconnectivityconstraint152.1.Multistagerandomgrowingsmall-Worldnetworkswithpower-lawdegreedistributionLiuJian-Guo,DangYan-ZhongandWangZhong-Tuo,ChinesePhysicsLetters23(3)746-749(2006)Onenodeisaddedineachtimestep；Selectthenodeuaccordingtothepreferentialmechanism；Selectaneighbornodeofnodeu；1617Onenodeisaddedineachtimestep；Selectthenodeuaccordingtothepreferentialmechanism；Selectaneighbornodeofnodeuaccordingtops；2.2.Growingscale-freenetworkmodelwithtunableassortativecoefficientQiangGuo,TaoZhou,Jian-GuoLiuetal.,PhysicaA371814-822(2006)18192.3Self-learningmutualselectionmodelforweightednetworksJian-GuoLiuetal.,DCDISBSupplement,ComplexNetworks,14(S7)33-36,(2007).123412345m=21234520212.4RandomEvolvingNetworksUndertheDiameterandAverageConnectivityConstraintThegrowthofrandomnetworksundertheconstraintthatthediameter,definedastheaverageshortestpathlengthbetweenallnodes,andtheaverageconnectivityremainsapproximatelyconstantisstudied.Weshowedthat,ifthenetworkmaintainstheformofitsdegreedistributionandthemaximaldegreeisaN-dependentcutofffunction,thenthedegreedistributionwouldbeapproximatelypower-lawwithanexponentbetween2and3.Jian-GuoLiuetal.,JournalofSystemScienceandSystemEngineering16(1)107-112(2007).22MotivationInthebiologicalnetworks,theconstantdiametermayberelatedtoimportantpropertiesofthesebiologicalnetworks,suchasthespreadandspeedofresponsestoperturbations.IntheInternetbackbonenetwork,theaveragedistanceisoneofthemostimportantfactorstomeasuretheefficiencyofcommunicationnetwork,anditplaysasignificantroleinmeasuringthetransmissiondelay.Theseconstraintscanbethoughtofastheenvironmentalpressures,whichwouldselecthighlyefficientstructuretoconveythepacketsinit.23Motivation24ConstructionofthemodelTheexpressionforthediameterdofarandomnetworkwitharbitrarydegreedistributionwasdevelopedWhereistheaveragedegree,25InordertoseekadegreedistributionthatmaintainsitsdistributionandhasanapproximatelyconstantdiameterindependentofN.TheparameterNcanbeaccomplishedbyimposingaN-dependentcutofffunction26Thedistributionp(k)canbedeterminedbywritingthisequationforandAlgebraicmanipulationyieldstherelation27Usinganintegralapproximation,amoreexplicitformulationcanbewrittenasfollowing.28Whenthenumericallycalculateddegreedistributionsforvariousvaluesof29DiscussionofparttwoWehavepresentedareasonfortheexistenceofpower-lawdegreedistributionunderthediameterconstraintobservedintheInternetbackbonenetworkwherethereareevolutionarypressurestomaintainitsdiameter.Ouranalysisshowsthat,ifthemaximaldegreeisaN-dependentcutofffunction,theformofarobustnetworkdegreedistributionshouldbepowerlawtomaintainitsdiameter,whiletheaverageconnectivitypernodeaffectthedistributionexponentslightly.30OutlineBackgroundintroductionNetworkevolutionmodelsDynamicalpropertiesoncomplexnetworksPersonalizedrecommendation313.1Structuraleffectsonsynchronizabilityofscale-freenetworks323.1HowtomeasurethesynchronizabilityWhereQistheratiooftheeigenvalues.ThesynchronizabilitywouldbeincreasedasQdecreases,viceverse.33Theedgeexchangemethodisintroducedtoadjustthenetworkstructure,andthetabusearchalgorithmisusedtominimizetheeigenvalueratioQminQiangGuo,LiuJian-Guo,etal,ChinesePhysicsLetters24(8)(2007)2437-2440.34Insummary,usingthetabuoptimalalgorithm,wehaveoptimizednetworksynchronizabilitybychangingtheconnectionpatternbetweendifferentpairsofnodeswhilekeepingthedegreedistribution.Startingfromscale-freenetworks,wehavestudiedthedependencebetweenthestructuralcharacteristicsandsynchronizability.Thenumericalresultssuggestthatascale-freenetworkwithshorterpathlength,lowerdegreeofclustering,anddisassortivepatterncanbeeasilysynchronized.353.1StructuraleffectsonsynchronizabilityminmaxCombiningthetabusearch(TS)algorithmandtheedgeexchangemethod,weenhanceandweakenthesynchronizabilityofscale-freenetworkswithdegreesequencefixedtofindthestructuraleffectsofthescale-freenetworkonsynchronizabilityLiuJian-Guo,etal,InternationalJournalofModernPhysicsC18(7)1087-1094(2008).36ThenumericalresultsindicatethatD,C,randBminfluencesynchronizabilitysimultaneously.Especially,thesynchronizabilityismostsensitivetoBm.37Effectoftheloopstructureonsynchronizability38OutlineBackgroundintroductionNetworkevolutionmodelsDynamicalpropertiesoncomplexnetworksPersonalizedrecommendation39PersonalizedrecommendationImprovedcollaborativefilteringalgorithmbasedoninformationtransaction.Ultraaccuracyrecommendationalgorithmbyconsideringthehigh-orderusersimilaritiesEffectofusertastesonpersonalizedrecommendation40WhyrecommendWefacetoomuchdataandsourcestobeabletofindoutthosemostrelevantforus.Indeed,wehavetomakechoicesfromthousandsofmovies,millionsofbooks,billionsofwebpages,andsoon.Evaluatingallthesealternativesbyourselvesisnotfeasibleatall.Asaconsequence,anurgentproblemishowtoautomaticallyfindouttherelevantobjectsforus.41CollaborativefilteringalgorithmHerlockeretal.,ACMTrans.Inf.Syst.22:5-53(2004)42Content-basedalgorithmTheuserwillberecommendeditemssimilartotheonesthisuserpreferredinthepastPazzani&Billsus,LNCS4321:325-341(2007)43ImprovedcollaborativefilteringalgorithmbasedoninformationtransactionIntraditionalCFalgorithm,Firstly,theusersimilarityiscomputedbasedonthePearsoncoefficientThengivethepredictedscoretotheuncollectedobjectsbasedontheusersimilaritiesByusingthediffusionprocesstocomputetheusersimilaritytoimproveCFalgorithm44Iliustrationofthediffusion-basedusersimilarityThetargetuserisactivatedandbeassignedaunitrecommendationpower,thenthemassisdiffusedfromthetargetusertotheobjectshehascollected,thentheit’’sdiffusedbackfromtheobjectstotheusers.Jian-GuoLiuetal,InternationalJournalofModernPhysicsC20285(2009).45TwoimprovedalgorithmsWearguethatthepotentialroleoftheobjectdegreesshouldbetakenintoaccounttoregulatetheusersimilarityOnlythetop-Nmostsimilarusers’opinionaretakenintoaccounttosavethememoryandincreasethecomputationspeed.46Numericalresultsoftheaveragerankingscore47Diversity48Averagerankingscoreofthetop-Nalgorithm49ConclusionanddiscussionsUsingthediffusionprocesstocomputetheusersimilaritycouldimproveCFalgorithmicaccuracyThecomputationalcomplexityofthepresentedalgorithmismuchlessthanthatofthestandardCF.Boththetwomodifiedalgorithmcanfurtherenhancetheaccuracy.WithproperlychoiceoftheparameterN,top-Nalgorithmcansimultaneouslyreducesthecomputationalcomplexityandimprovesthealgorithmicaccuracy.502,Ultraaccuracyrecommendationalgorithmbyconsideringthehigh-orderusersimilaritiesThemainideaFigure1showsanillustration,where1denotesthemainstreampreferencesharedbyallA,BandC,and2isthespecificpreferenceofAandC.Both1and2contributetothecorrelationbetweenAandC.Since1isthemainstreampreference,italsocontributestothecorrelationsbetweenAandB,aswellasBandC.TrackingthepathAtoBtoC,thepreference1alsocontributestothesecond-ordercorrelationbetweenAandC.Statisticallyspeaking,twouserssharingmanymainstreampreferencesshouldhavehighsecond-ordercorrelation,thereforewecandepresstheinfluenceofmainstreampreferencesbytakingintoaccountthesecond-ordercorrelation.Jian-GuoLiuetal,PhysicaA389881(2010).51ThepresentedalgorithmDenotetheusersimilaritymatrixiswhereHisthenewlydefinedcorrelationmatrix,S={}isthefirst-ordercorrelationdefinedasEq.(2),andisatunableparameter.Asdiscussedbefore,weexpectthealgorithmicaccuracycanbeimprovedatsomenegative.52Numericalresultsr5354EffectofusertastesonpersonalizedrecommendationWestudytheeffectsofusertastesonthemass-diffusion-basedpersonalizedrecommendationalgorithm,whereauser'stastesorinterestsaredefinedbytheaveragedegreeoftheobjectshehascollected.Wearguethattheinitialrecommendationpowerlocatedontheobjectsshouldbedeterminedbybothoftheirdegreeandtheusers'tastes.Byintroducingatunableparameter,theusertasteeffectsontheconfigurationofinitialrecommendationpowerdistributionareinvestigated.Jian-GuoLiuetal,InternationalJournalofModernPhysicsC20285(2009).55Numericalresults56AchievementsSelectedPublicationsAllpublicationshasbeencitedover118.H-indexis7Phys.Rev.E80,017101(2010);74,056109(2006).PhysicaA389,881(2010);371,861(2007);366,578(2006);371,814(2006);377,302(