基于相似性鏈接預(yù)測(cè)

EvaluationMetrics：AUC、LocalSimilarityIndices：CN、SaltonIndex、JaccardIndex、Srensen workG(V,E),whereVisthesetofnodesandEisthesetofNomultiplelinksandself-UdenotestheuniversalsetcontainingallpossibleU-EisthesetofnonexistentWedivideErandomlyintotwoparts：thetrainingset,,istreatedasknowninformation,whiletheprobeset,,isusedfortestingandnoinformationinthissetisallowedtobeusedforprediction.(statisticalerrorscanbe ebyusingtheK-foldcross-validation.)Evaluation1、Calculatethescoreofeachnon-observed2、Randomlypickamissinglinkandanonexistentlinktocomparetheirscores3、Amongntcomparisons,therearetimesthemissinglinkhavingahigherscoreandtimestheyhavethesamescore??′+??????4、Thedegreetowhichthevalueexceeds0.5indicateshowthealgorithmEvaluation1、Rankthenon-observed2、Takethetop-Llinksasthepredictedones,amongwhichlinksareright(thereare????linksintheprobeset 左圖有6個(gè)節(jié)點(diǎn)，10條邊和5條不存在的邊(1，2)、(1，4)、(1，5)、(2，5)和(2，6)。為了檢驗(yàn)算法的準(zhǔn)確性，邊(2，3)和(4，6)作為測(cè)試邊集測(cè)到的邊為(1，2)，(1，4)，(1，5)，(2，5)，(2，6)，(2，3)和(4，6)。LocalSimilarity==

Γ(??)∩Γ(??)denotethesetofneighborsof = = ??????=1ifxandyaredirectlyconnectedand??????=0LocalSimilarity==

Γ(??)∩where????isthedegreeofnode==

Γ(??)∩Γ(??)∪Srensen??Srensen=2Γ(??)∩ ????+LocalSimilarity Γ(??)∩ min{????, Γ(??)∩Γ(??) ??LHN1= LocalSimilarity

LocalSimilarityLuL,ZhouT.Link works:AGlobalSimilarity10、Katz∞??????????=?????? = + + +?

where????????? isthesetofallpathswithlength??connecting??and??,and??isdamparametercontrollingthepath??????????=(???????)Note:??mustbelowerthanthereciprocalofthelargesteigenvalueofmatrixAtoensuretheconvergenceofEq.GlobalSimilarityToprovideagoodtradeoffofaccuracyandcomputationalcomplexity,wetakeconsiderationoflocalpathswithwiderhorizonthanCN.??????=??2+??????(??)=??2+????3+??2??4+?+Theoptimalnispositivelycorrelatedwiththeaverageshortestdistanceofth GlobalSimilarity12、RandomWalkwithNode?? tivelymovestoarandomneighborwithprobabilitycandreturntonodewithprobability??????denotestheprobabilitythisrandomwalkerlocatesatnode??inthesteadystate,we??????

1???

???where??isthetransitionmatrixwith??????=1/????if??and??areconnected,and??????=???=(1???)(?????????)?1??????????= +??????isthe??thelementofthevector???.

GlobalSimilarity13、LocalRandom

=????????

+????????

=????0=???,??????+1=??????????GlobalSimilarity14、SuperposedRandom

=

=?????????

+????????GlobalSimilarityLuL,ZhouT.Link works:ALuL,ZhouT.Linkprediction works:Asurvey[J].PhysicaA-statisticalMechanicsandItsApplications,2010,390(6):ChebotarevP,ShamisE.TheMatrix- TheoremandMeasuringRelationsinSmallSocialGroups[J].Automatio