协同过滤外文文献翻译.docx

协同过滤外文文献翻译.docx

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协同过滤外文文献翻译

外文：

IntroductiontoRecommenderSystem

ApproachesofCollaborativeFiltering:

NearestNeighborhoodandMatrixFactorization

“Weareleavingtheageofinformationandenteringtheageofrecommendation.”

Likemanymachinelearningtechniques,arecommendersystemmakespredictionbasedonusers’historicalbehaviors.Specifically,it’stopredictuserpreferenceforasetofitemsbasedonpastexperience.Tobuildarecommendersystem,themosttwopopularapproachesareContent-basedandCollaborativeFiltering.

Content-based approachrequiresagoodamountofinformationofitems’ownfeatures,ratherthanusingusers’interactionsandfeedbacks.Forexample,itcanbemovieattributessuchasgenre,year,director,actoretc.,ortextualcontentofarticlesthatcanextractedbyapplyingNaturalLanguageProcessing. CollaborativeFiltering,ontheotherhand,doesn’tneedanythingelseexceptusers’historicalpreferenceonasetofitems.Becauseit’sbasedonhistoricaldata,thecoreassumptionhereisthattheuserswhohaveagreedinthepasttendtoalsoagreeinthefuture.Intermsofuserpreference,itusuallyexpressedbytwocategories. ExplicitRating,isarategivenbyausertoanitemonaslidingscale,like5starsforTitanic.Thisisthemostdirectfeedbackfromuserstoshowhowmuchtheylikeanitem. ImplicitRating,suggestsuserspreferenceindirectly,suchaspageviews,clicks,purchaserecords,whetherornotlistentoamusictrack,andsoon.Inthisarticle,Iwilltakeacloselookatcollaborativefilteringthatisatraditionalandpowerfultoolforrecommendersystems.

NearestNeighborhood

ThestandardmethodofCollaborativeFilteringisknownas NearestNeighborhood algorithm.Thereareuser-basedCFanditem-basedCF.Let’sfirstlookat User-basedCF.Wehaveann×mmatrixofratings,withuseruᵢ,i=1,...nanditempⱼ,j=1,…m.Nowwewanttopredicttheratingrᵢⱼiftargetuserididnotwatch/rateanitemj.Theprocessistocalculatethesimilaritiesbetweentargetuseriandallotherusers,selectthetopXsimilarusers,andtaketheweightedaverageofratingsfromtheseXuserswithsimilaritiesasweights.

Whiledifferentpeoplemayhavedifferentbaselineswhengivingratings,somepeopletendtogivehighscoresgenerally,someareprettystricteventhoughtheyaresatisfiedwithitems.Toavoidthisbias,wecansubtracteachuser’saverageratingofallitemswhencomputingweightedaverage,andadditbackfortargetuser,shownasbelow.

Twowaystocalculatesimilarityare PearsonCorrelation and CosineSimilarity.

Basically,theideaistofindthemostsimilaruserstoyourtargetuser（nearestneighbors）andweighttheirratingsofanitemasthepredictionoftheratingofthisitemfortargetuser.

Withoutknowinganythingaboutitemsandusersthemselves,wethinktwousersaresimilarwhentheygivethesameitemsimilarratings.Analogously,for Item-basedCF,wesaytwoitemsaresimilarwhentheyreceivedsimilarratingsfromasameuser.Then,wewillmakepredictionforatargetuseronanitembycalculatingweightedaverageofratingsonmostXsimilaritemsfromthisuser.OnekeyadvantageofItem-basedCFisthestabilitywhichisthattheratingsonagivenitemwillnotchangesignificantlyovertime,unlikethetastesofhumanbeings.

Therearequiteafewlimitationsofthismethod.Itdoesn’thandlesparsitywellwhennooneintheneighborhoodratedanitemthatiswhatyouaretryingtopredictfortargetuser.Also,it’snotcomputationalefficientasthegrowthofthenumberofusersandproducts.

MatrixFactorization

SincesparsityandscalabilityarethetwobiggestchallengesforstandardCFmethod,itcomesamoreadvancedmethodthatdecomposetheoriginalsparsematrixtolow-dimensionalmatriceswithlatentfactors/featuresandlesssparsity.ThatisMatrixFactorization.

Besidesolvingtheissuesofsparsityandscalability,there’sanintuitiveexplanationofwhyweneedlow-dimensionalmatricestorepresentusers’preference.AusergavegoodratingstomovieAvatar,Gravity,andInception.Theyarenotnecessarily3separateopinionsbutshowingthatthisusersmightbeinfavorofSci-FimoviesandtheremaybemanymoreSci-Fimoviesthatthisuserwouldlike.Unlikespecificmovies,latentfeaturesisexpressedbyhigher-levelattributes,andSci-Ficategoryisoneoflatentfeaturesinthiscase. Whatmatrixfactorizationeventuallygivesusishowmuchauserisalignedwithasetoflatentfeatures,andhowmuchamoviefitsintothissetoflatentfeatures. Theadvantageofitoverstandardnearestneighborhoodisthateventhoughtwousershaven’tratedanysamemovies,it’sstillpossibletofindthesimilaritybetweenthemiftheysharethesimilarunderlyingtastes,againlatentfeatures.

Toseehowamatrixbeingfactorized,firstthingtounderstandis SingularValueDecomposition（SVD）.BasedonLinearAlgebra,anyrealmatrixRcanbedecomposedinto3matricesU,Σ,andV.Continuingusingmovieexample,Uisann×ruser-latentfeaturematrix,Visanm×rmovie-latentfeaturematrix.Σisanr×rdiagonalmatrixcontainingthesingularvaluesoforiginalmatrix,simplyrepresentinghowimportantaspecificfeatureistopredictuserpreference.

TosortthevaluesofΣbydecreasingabsolutevalueandtruncatematrixΣtofirstkdimensions（ksingularvalues）,wecanreconstructthematrixasmatrixA.TheselectionofkshouldmakesurethatAisabletocapturethemostofvariancewithintheoriginalmatrixR,sothatAistheapproximationofR,A≈R.ThedifferencebetweenAandRistheerrorthatisexpectedtobeminimized.ThisisexactlythethoughtofPrincipleComponentAnalysis.

WhenmatrixRisdense,UandVcouldbeeasilyfactorizedanalytically.However,amatrixofmovieratingsissupersparse.Althoughtherearesomeimputationmethodstofillinmissingvalues,wewillturntoaprogrammingapproachtojustlivewiththosemissingvaluesandfindfactormatricesUandV.InsteadoffactorizingRviaSVD,wearetryingfindUandVdirectlywiththegoalthatwhenUandVmultipliedbacktogethertheoutputmatrixR’istheclosestapproximationofRandnomoreasparsematrix.Thisnumericalapproximationisusuallyachievedwith Non-NegativeMatrixFactorization forrecommendersystemssincethereisnonegativevaluesinratings.

Seetheformulabelow.Lookingatthepredictedratingforspecificuseranditem,itemiisnotedasavectorqᵢ,anduseruisnotedasavectorpᵤsuchthatthedotproductofthesetwovectorsisthepredictedratingforuseruonitemi.ThisvalueispresentedinthematrixR’atrowuandcolumni.

Howdowefindoptimalqᵢandpᵤ?

Likemostofmachinelearningtask,alossfunctionisdefinedtominimizethecostoferrors.

rᵤᵢisthetrueratingsfromoriginaluser-itemmatrix.OptimizationprocessistofindtheoptimalmatrixPcomposedbyvectorpᵤandmatrixQcomposedbyvectorqᵢinordertominimizethesumsquareerrorbetweenpredictedratingsrᵤᵢ’andthetrueratingsrᵤᵢ.Also,L2regularizationhasbeenaddedtopreventoverfittingofuseranditemvectors.It’salsoquitecommontoaddbiastermwhichusuallyhas3majorcomponents:

averageratingofallitemsμ,averageratingofitemiminusμ（notedasbᵤ）,averageratinggivenbyuseruminusu（notedasbᵢ）.

Optimization

AfewoptimizationalgorithmshavebeenpopulartosolveNon-NegativeFactorization. AlternativeLeastSquare isoneofthem.Sincethelossfunctionisnon-convexinthiscase,there’snowaytoreachaglobalminimum,whileitstillcanreachagreatapproximationbyfindinglocalminimums.AlternativeLeastSquareistoholduserfactormatrixconstant,adjustitemfactormatrixbytakingderivativesoflossfunctionandsettingitequalto0,andthensetitemfactormatrixconstantwhileadjustinguserfactormatrix.Repeattheprocessbyswitchingandadjustingmatricesbackandforthuntilconvergence.IfyouapplyScikit-learnNMFmodel,youwillseeALSisthedefaultsolvertouse,whichisalsocalledCoordinateDescent.PysparkalsooffersprettyneatdecompositionpackagesthatprovidesmoretuningflexibilityofALSitself.

SomeThoughts

CollaborativeFilteringprovidesstrongpredictivepowerforrecommendersystems,andrequirestheleastinformationatthesametime.However,ithasafewlimitationsinsomeparticularsituations.

First,theunderlyingtastesexpressedbylatentfeaturesareactuallynotinterpretablebecausethereisnocontent-relatedpropertiesofmetadata.Formovieexample,itdoesn’tnecessarilytobegenrelikeSci-Fiinmyexample.Itcanbehowmotivationalthesoundtrackis,howgoodtheplotis,andsoon.CollaborativeFilteringislackoftransparencyandexplainabilityofthislevelofinformation.

Ontheotherhand,CollaborativeFilteringisfacedwithcoldstart.Whenanewitemcomingin,untilithastoberatedbysubstantialnumberofusers,themodelisnotabletomakeanypersonalizedrecommendations.Similarly,foritemsfromthetailthatdidn’tgettoomuchdata,themodeltendstogivelessweightonthemandhavepopularitybiasbyrecommendingmorepopularitems.

It’susuallyagoodideatohaveensemblealgorithmstobuildamorecomprehensivemachinelearningmodelsuchascombiningcontent-basedfilteringbyaddingsomedimensionsofkeywordsthatareexplainable,butweshouldalwaysconsiderthetradeoffbetweenmodel/computationalcomplexityandtheeffectivenessofperformanceimprovement.

中文翻译

推荐系统介绍

协同过滤的方法：

最近邻域和矩阵分解

“我们正在离开信息时代，而进入推荐时代。

”

像许多机器学习技术一样，推荐系统根据用户的历史行为进行预测。

具体来说，是根据过去的经验来预测用户对一组商品的偏好。

要构建推荐系统，最流行的两种方法是基于内容的过滤和协作过滤。

基于内容的方法需要大量项目自身功能的信息，而不是使用用户的交互和反馈。

例如，它可以是电影属性（例如流派，年份，导演，演员等）或可以通过应用自然语言