Flexible Mixture Model for Collaborative Filtering

Transcription

1 Feibe Miue Mode fo Coaboaive Fieing uo Si ong Jin Schoo of Compue Science Canegie Meon Univesi isbugh A 5232 USA SI@CS.CMU.EDU ONG@CS.CMU.EDU Absac This pape pesens a feibe miue mode FMM fo coaboaive fieing. FMM eends eising paiioning/cuseing agoihms fo coaboaive fieing b cuseing boh uses and iems ogehe simuaneous wihou assuming ha each use and iem shoud on beong o a singe cuse. Fuhemoe wih he inoducion of pefeence nodes he poposed famewok is abe o epici mode how uses ae iems which can va damaica even among he uses wih simia ases on iems. Empiica sud ove wo daases of movie aings has shown ha ou new agoihm oupefoms five ohe coaboaive fieing agoihms subsania.. Inoducion The apid gowh of he infomaion on he Inene demands ineigen infomaion agen ha can sif hough a he avaiabe infomaion and find ou he mos vauabe o us. These ineigen ssems can be caegoied ino wo casses: coaboaive fieing Beese Heckeman & Kadie 998 and conen-based ecommending Basu & Hish 998. The diffeence beween coaboaive fieing and conen-based ecommending is ha: coaboaive fieing on uiies he aings of aining uses in ode o pedic aings fo es uses whie conen-based ecommendaion ssems e on he conens of iems fo pedicions. Theefoe coaboaive fieing ssems have advanages in he envionmens whee he conens of iems ae no avaiabe due o pivac issues o whee ha conens ae difficu fo a compue o anae. In his pape we on focus on he coaboaive fieing pobems. Mos coaboaive fieing mehods fa ino wo caegoies: memo-based agoihms and mode-based agoihms. Memo-based agoihms usua do no have a aining phase. Insead he simp soe aing eampes of uses ino a aining daabase. In he pedicing phase he memo-based appoaches fis find uses in he aining daabase simia o he es use and hen pedic he es use s aings based on he coesponding aings of hese simia uses. On he cona mode-based agoihms buid modes ha ae abe o epain he aining eampes we and pedic he aings of es uses using he esimaed modes. Boh of he memo-based agoihms and he mode-based agoihms have hei advanages and disadvanages. Memo-based agoihms have much ess off-ine compuaion coss whie he mode-based agoihms ma have ess on-ine compuaion coss. Though memo-based and mode-based appoaches diffe fom each ohe in man aspecs boh of hem assume ha uses wih simia ases shoud ae iems simia and heefoe he idea of cuseing is used in boh appoaches eihe epici o impici. Fo memo-based appoaches aining uses simia o he es use ae gouped ogehe and hei aings ae combined o pedic aings fo he es use. Meanwhie mode-based appoaches cuse iems and/o aining uses ino casses epici and pedic aings of a es use b simp using he aings of casses ha fi in bes wih he es use and/o iems o be aed. Thus how o cuse uses and iems appopiae is a ke issue in designing coaboaive fieing ssems which can affec he scaabii obusness and pefomance. Whie heoeica ineesing mode-based appoaches have achieved mied esus in pevious sudies Beese e a. 998; O Conno & Heocke 200. We suspec ha his ma be due o he inappopiae cuseing agoihms used in hei sudies. Moe specifica hee issues of cuseing agoihms ae impoan fo coaboaive fieing: Fis boh uses and iems need o be cuseed and moe impoan uses and iems ae couped wih each ohe hough he aing infomaion. Theefoe a good cuseing agoihm shoud be abe o epici mode boh casses of uses and iems and be abe o eveage hei coeaion. Second man cuseing echniques assume ha each use o iem beongs o a singe cass. Howeve since a use ma have divese ineess and an iem ma have muipe aspecs i is desiabe o aow boh iems and uses o be in muipe oceedings of he Twenieh Inenaiona Confeence on Machine eaning ICM-2003 Washingon DC 2003.

2 casses simuaneous. In his pape a feibe miue mode FMM is poposed in ode o capue his idea. Thid he assumpion ha uses wih simia ases woud have simia aings ma no necessai be ue because some uses ma end o give a highe aing o a iems han some ohes. In ode o accoun fo he vaiance in he aing paens among he uses wih simia ineess we eend he feibe miue mode b inoducing an addiiona new hidden pefeence node. Such an eension aows us o infe he pefeence vaues undeing he suface aings which can hen be used as pesumab moe eiabe evidence fo cuseing. Fo he simpici of compuaion we compue he pefeence infomaion fo each use using decouped modes DM and hen app he poposed feibe miue mode o cuse ove he esimaed pefeence vaues insead of he oigina aing vaues. The es of he pape is aanged as foows: Secion 2 discusses pevious wok. The poposed feibe miue mode fo coaboaive fieing is pesened in Secion 3. The eended vesion of feibe miue mode wih he decouping of aing and pefeence is discussed in Secion 4. Secion 5 pesens epeimens esus. Concusions and fuue wok ae discussed in Secion Eising Appoaches e us fis inoduce he annoaions ha wi be used fo he es of his pape. e {... M } be a se of iems Y {... N } be a se of uses and {... } be a se of aings. e {... } be he aings infomaion in he aining daabase be he se of iems aed _ b use be he aing of iem b use and be he aveage aing b use. 2. Memo-Based Agoihms Two common used memo-based agoihms ae eason Coeaion Coefficien agoihm CC esnick e a. 994 and Veco Space Simiai VS Beese Heckeman & Kadie 998 agoihm. The main idea of hese wo agoihms is o cacuae he simiaiies of he aining uses o he es use and he pedicion of aings is compued b pefoming a weighed aveage of deviaions fom he aining uses mean. The diffeence beween hem is on how o compue he simiaiies beween uses whee a eason coeaion coefficien is used fo measuing he use simiai in he CC agoihm and a cosine simiai is compued in he VS agoihm. Moe deais can be found in esnick e a. 994; Beese Heckeman & Kadie Mode-Based Agoihms Thee mode-based agoihms ae discussed hee: he aspec mode AM Hofmann & uicha 999 wosided cuseing mode Hofmann & uicha 999 and he esonai Diagnosis mode D ennock e a Aspec Mode AM The aspec mode Hofmann & uicha 999 is a pobabiisic aen space mode which modes individua pefeences as a conve combinaion of pefeence facos. The aen cass vaiabe { 2... K} is associaed wih each obsevaion pai of a use and an iem. The aspec mode assumes ha uses and iems ae independen fom each ohe given he aen cass vaiabe. Thus he pobabii fo each obseved pai is cacuaed as foows: whee sands fo cass pio pobabii and sand fo cass dependen disibuions fo iems and uses especive. Essenia he pefeence paen of a use is modeed b a combinaion of pica pefeence paens which ae epesened b he disibuions of and. Noe ha he aspec mode on inoduces one se of aen vaiabes fo he pupose of cuseing and hee is no epici gouping of eihe uses o iems. In he poposed mode we ineniona inoduce wo ses of aen vaiabes in ode o mode he cuses of uses and he cuses of iems sepaae. Two of he choices Hofmann & uicha 999 o incopoae he aings ino he aspec mode ae epessed in Equaion 2 and 3 especive. 2 3 The coesponding gaphica modes fo Equaion 2 and 3 ae shown in Figue as mode a and b especive. Accoding o he gaphic modes he diffeence beween hese wo mehods is ha in he gaphic mode a o Equaion. 2 he aing is condiioned on on he aen cass vaiabe whie he second mode e he aing be condiioned on boh he aen cass vaiabe and he iem. The second mode is a efined vesion of he fis mode bu he numbe of paamees is much age han he fis mode wih he same numbe of aspecs. Two-Sided Cuseing Mode A wo-sided cuseing mode is poposed fo coaboaive fieing in Hofmann & uicha 999. This mode assumes ha each use shoud beong o eac one goup of uses and he same is ue fo each iem. e C { c... c I } be he casses of uses and D d... d } be he casses of iems. Indicao { J

3 a vaiabes I iv and J ju {0 } indicaes whehe he ih use beongs o he vh use cass and he jh iem beongs o he uh iem cass especive. Then he join pobabii is defined as: I vj uc vu 4 v u Cvu is he cuse associaion paamee. In ode o be consisen wih he above assumpion a goba nomaiaion consain has o be made as IvJ ucvu 5 v u Hofmann & uicha 999 poined ou ha his mode has a diffeen spii fom he aspec mode and is ess feibe in modeing he pefeences eaionship beween he uses and iems and we beieve he ke eason is is song assumpion. Howeve his mode does o mode he cuseing of uses and iems sepaae which appeas o be a bee modeing appoach. Since pevious epeimens have shown ha he pefomance of aspec mode is subsania bee han he wo-sided cuseing mode we wi no compae ou mode wih he wo-sided cuseing mode. esonai Diagnosis Mode D Y Figue. Gaphica modes fo he wo eensions of aspec mode in ode o capue aing vaues. In he pesonai diagnosis mode ennock e a he obseved aing fo he es use on an iem is assumed o be dawn fom an independen noma disibuion wih he mean as he ue aing as Tue Tue 2 2 Tue 2σ e : whee he sandad deviaion σ is se o consan in ou epeimens. Then he pobabii of geneaing he obseved aing vaues of he es use b an use in he aining daabase can be wien as: b Y 6 e 2 2 2σ The ikeihood fo he es use o ae an unseen iem as caego can be compued as: 2 Tue 2 2σ e 8 The fina pediced aing fo iem b he es use wi be he aing caego wih he highes ikeihood Tue. Empiica sudies have shown ha he D mehod is abe o oupefom sevea ohe appoaches fo coaboaive fieing ennock e a The Feibe Miue Mode FMM In his secion we inoduce he feibe miue mode FMM and show how i can be appied o he coaboaive fieing ask. 3. Mode Descipion The FMM fo coaboaive fieing is moivaed b he foowing obsevaions on he wo-sided cuseing mode and he aspec mode. Compaed wih he wo-side cuseing mode he aspec mode has he feibii of eing each use and iem beong o muipe goups simuaneous whie he wo-sided cuseing mode esics each use and iem o be in eac one cuse. This issue can be quie impoan fo he coaboaive fieing ask because hee ma no be a se of undeing cuses fo uses and iems ha ae ecusive fom each ohe. Mos ike we wi see oveapping cuses which ead o muipe membeships fo uses and iems. Fo eampe he fim Toa! Toa! Toa! ma be deemed as a wa movie b a oung man due o is inensive wa scenes whie a veean ma ea i as a hisoica fim because of he hisoica evens descibed in he movie. Cea he non-ecusive naue beween he caego hisoica movie and wa movie eads o he muipe membeship fo his movie. On he ohe hand he wo-sided cuseing mode is abe o epici mode he cuses of uses and iems which appeas o make sense. Based on hese obsevaions we popose he feibe miue mode FMM fo coaboaive fieing which ies o addess he wo issues name aowing each use and iem o be in muipe cuses and modeing he cuses of uses and iems sepaae. e C { c... c I } be he casses of uses and D { d... d J } be he casses of iems; aen vaiabe indicaes he cass membeship fo use and I is a muinomia disibuion on he use casses; aen vaiabe indicaes he cass membeship fo iem and J is a muinomia disibuion on he iem casses; Y 7

4 N Y I is a muinomia disibuion descibing he condiiona pobabii of uses Y given a specific use cass ; M J is a muinomia disibuion descibing he condiiona pobabii of iems given a specific iem cass ; I J is a muinomia disibuion fo he aings given a specific use cass and a specific iem cass. Wih above annoaion he join geneaion pobabii fo FMM can be wien as: 9 The coesponding gaphica mode is shown in Figue 2. Accoding o he mode he FMM diffes fom he aspec mode in ha i epici modes he use casses and he iems casses wih wo ses of aen vaiabes { } and { }. The FMM mode is diffeen fom he wo-sided cuseing mode b he fac ha i does no have he goba nomaiaion esicion in Equaion 5. The gaphica mode mos simia o he poposed FMM mode is he poduc space miue mode SMM Hofmann & uicha 998 which was poposed fo infomaion eieva. Bu he SMM mode on eends he aspec mode b enfocing a decomposiion of aspecs ha sum up o whie ou FMM has wo ses of aen vaiabes and which nomaied sepaae. 3.2 The Taining ocedue The Epecaion and Maimiaion EM Dempse & ubin 977 agoihm is a we-known opimiaion agoihm which aenaes beween wo seps: In he epecaion sep he join poseio pobabiiies of he aen vaiabes { } ae compued; in he maimiaion sep he mode paamees ae updaed given he poseio pobabiiies esimaed in he epecaion sep. Moe specifica in he epecaion sep he join poseio pobabiiies ae compued as: 0 Then he mode paamees ae updaed in he maimiaion sep as: 2 : 3 : 4 : 5 In ode o avoid he unfavoabe oca maimum pobems we use a genea fom of he EM agoihm named anneaed EM agoihm AEM Hofmann & uicha 998 which is an EM agoihm wih eguaiaion. In his agoihm he aining daabase is divided ino wo pas: he aining daa and he hed-ou daa. In he epecaion sep a vaiabe b is inoduced o cono he aining pocess as: b b 6 When vaiabe b goes o posiive infini he poseio pobabii becomes a dea funcion and he cuseing pocess becomes he had case each use and iem beong o a singe cass. When vaiabe b is se o he AEM euns back o he oigina EM agoihm in Equaion 0. Theefoe b vaing he vaiabe b we can adjus he cuseing pocess. In ou pocedue b is iniia se o. We pefom EM agoihm wih ea sopping if he pefomance on hod-ou daa deeioaes. Then he vaiabe b is deceased b0.9*b and he EM is appied again uni b is smae han a owe bound 0.5. Fina a new mode is ained ove he whoe aining daa incuding he hed-ou daase wih he cuen b vaue fo sevea seps. A simia aining pocedue is appied o ain he aspec modes as descibed in Secion The edicion ocedue The uimae goa of he coaboaive fieing is o pedic aings fo he es use on unseen iems given a se of obseved aings of he es use : Figue 2. Gaphica mode epesenaion fo he feibe miue mode FMM. Y

5 {.. N _ G N _ G } whee N_G sands fo he numbe of given aings of he es use. A fod-in pocess can be used o make he pedicion. The main idea of his pocess is o esimae he join pobabii of he aing iem and he es use as and o pedic he aing wih he epecaion as. The join pobabii is cacuaed as: 7 We have a he vaiabes on he igh hand side of Equaion 7 fom he aining pocess ecep which can be compued b simp eaing he es use as anohe use in he aining daabase and un he EM agoihm as descibed above wih a he paamees fied ecep. Wih he esimaed join pobabii he pedicion of aing on iem can be compued as: ' 8 ' 4. The Combinaion of FMM and he Decouped Modes of efeences and aings The ohe ke issue wih he coaboaive fieing is ha uses wih simia o even idenica ase pefeence on he iems ma give ve diffeen suface aings. Fo eampe wo movie viewes A and B ma have eac he same ase on he fims which means he boh ike he same se of fims and disfavo anohe same se of fims. Bu he viewe A can be quie sic on his aing sandad and ma ae mos of his favoie fims on as aing 3 and ae a of his disfavoed fims wih aing. On he hand he viewe B is a quie oeaing peson and ma ae mos of his favoie fims wih highes aing 5 and even ae his disfavoed fims wih aing 3. In ode o accoun fo he vaiance in he aing behavio among he uses wih simia ineess we eend he gaphica mode in Figue 2 b inoducing a new aen node V which accouns fo he ue pefeence vaues and node which accouns fo diffeen aing behavios. Fis accoding o Figue 3 he use node Y is deemined join b nodes and name uses ae disinguished fom each ohe boh b hei ineess encode in and b hei aing paens encoded in. Second he pefeence node V is deemined join b he node and node e.g. v. Thid he aing is geneaed b he pefeence node and he node. Theefoe i is no necessa ha an iem wih a high aing be u favoed b he use due o he dependenc of node and. Fina in he eended vesion of FMM mode wo aen vaiabes and ae no couped hough he aing infomaion as in Figue 2. Insead he ae conneced diec hough he pefeence node V and he aing infomaion can infuence he coeaion beween nodes and indiec hough he pefeence node V. e he pefeence vaiabe V be a coninuous andom vaiabe anging fom 0 o e.g. 0 v. Wih he new gaphic mode he join pobabii can be cacuaed as: v v v v V 9 whee and v ae muinomia disibuions and v is noma disibuion. v Figue 3. Gaphica mode epesenaion of he eension of feibe miue mode o goup aing paens. Unfounae due o he inoducion of he pefeence node V and he aen aing node he infeence and pedicion pocesses ae ahe compe and imeconsuming. Consideing ha he coaboaive fieing ask usua demands high efficienc insead of using he above compe gaphica mode diec we epoe a simpe mode ha is abe o compue he pefeence vaues fo a use given a se of aed iems of ha use. Wih his simpe mode we ae abe o obain he pefeence vaue v diec insead of having o infe i fom he gaphic mode in Figue 3. Then a FMM mode simia o Figue 2 can be used fo compuing he aings fo he es use b simp epacing he aing node wih he pefeence node V. 4. The Decouped Modes of efeences and aings So we need o cacuae he pefeence vaue on an iem wih specific aing fo a use who gives a se of aed Y

6 iems. Two facos can infuence his vaue: he pecenage of iems ha have been aed no moe han. The age he numbe of iems aed no moe han he moe ike ha he use pefes he iem. 2 The pecenage of iems ha have been aed as. The age he numbe of iems aed as he ess ike ha he iem is pefeed b he use. Based on his inuiion we e _ 0 _ {.. } be he ikeihood funcion fo use on an iem which he aes wih aing ; he veco C { c... c } sand fo he aing coun veco which couns how man imes he use has aed iems wih specific aings. _ is compued as: _ aing aing / 2 c ' c ' c '' 2 * '' '' c '' 20 This pocedue can be seen in anohe wa as somehow nomaiing he use aings ino use pefeence. When hee ae ve few given aings fom he use Equaion 20 ma become uneiabe. A bee souion is a smoohed vesion of he aing funcion which uiies he aing paens of simia uses. The simiai coefficien beween he use and is defined as he pobabii of misaking use given he aing paens of use : C ' ' C ' w ' ' C 2 C '' '' C '' '' The as sep is deived b assuming a unifom disibuion on. And C ' is compued as: C ' c' c' ' ' aing '' C The smoohed vesion of is as foows: ' aing w aing + ' Y w + w ' ' Y w ' aing ' ugging Equaion 23 ino Equaion 20 we can conve a aing given b a use ino he ikeihood of being pefeed. Now e us conside he opposie name how o conve an esimaed ikeihood of being pefeed V ino an appopiae aing. We simp find he ank ha eads o he pefeence pobabii _ coses o he esimaed pefeence vaue V : ag min _ V The Combinaion of he FMM and he DM The basic idea of combining FMM wih he decouped modes DM is o fis conve he aings in he aining daabase ino hei coesponding pefeence vaues using he DM mode. Then simia o he gaphic mode in Figue 2 a FMM is bui ove pefeence vaues insead of he aings e.g. epacing he aing node wih he pefeence node V in Figue 2. Moe specifica he join pobabii v fo a use an iem and a pefeence vaue v is compued as: v v 25 whee v is he pefeence vaue compued fom Equaion 20. Compaed wih Equaion 0 Equaion 25 conains em v insead of. Fo simpici we assume v o be a noma disibuion i.e. v ep 2 2σ 2 v u 2πσ 26 The updaing equaions fo he means and sandad deviaions ae deived b AEM agoihm in Secion 3.2. Wih his modified FMM mode using pefeence vaue we wi be abe o compue he esimaed pefeence vaue v fo an iem given he use e.g. V. The fina aing is compued b conveing he esimaed pefeence vaue V ino aing using Equaion Epeimens In his secion we wi pesen epeimen esus in ode o addess wo issues. Is he FMM moe effecive han ohe coaboaive fieing agoihms? In he epeimen we wi compae he poposed FMM mode o ohe popua agoihms. 2 Can he FMM be fuhe impoved b combining i wih he decouped modes DM as discussed in Secion 4? In he epeimen we wi compae he pefomance of FMM wih and wihou he decouped modes DM. Two daases of movie aings ae used in ou epeimens. The fis one is he Movieaing esbed. The second esbed comes fom he EachMovie 2 whee a subse of 2000 uses wih moe han 40 aings was eaced. The deais of hese wo daases ae ised in Tabe. To compae diffeen agoihms in a age specum we ied sevea diffeen configuaions. Fo he Movieaing esbed we se he fis 00 o 200 uses o be he aining uses. Fo he EachMovie esbed he fis 200 o 400 uses wee used. Fuhemoe 5 0 o 20 hp:// 2 hp://eseach.compaq.com/sc/eachmovie

7 Tabe. Chaaceisics of he Movieaing Tesbed and he EachMovie Tesbed. Movieaing EachMovie Numbe of Uses Numbe of Iems Aveage Numbe of aed Iems e Use Numbe of aings 5 6 Tabe 2. Epeimen esus MAE on he Movieaing Tesbed. A smae vaue means a bee pefomance. Taining Uses Sie Agoihms 5 Iems 0 Iems 20 Iems CC VS D AM_a AM_b FMM CC VS D AM_a AM_b FMM Tabe 3. Epeimen esus MAE on he EachMovie Tesbed. A smae vaue means a bee pefomance. Taining Uses Sie Agoihms 5 Iems 0 Iems 20 Iems CC VS D AM_a AM_b FMM CC VS D AM_a AM_b FMM iems wee povided as eposed iems fo a es use on boh hese wo esbeds. As we beieve ha i is had fo coaboaive fieing ssem o coec huge amoun of aining daa befoe i can povide ecommendaion sevice o he cusomes so i is moe impoan o evauae he ssem pefomance wih a imi numbe of aining uses a eaive sma numbe of aining uses wee used in ou epeimens. Bu ohe epeimens wih moe aining uses 300 and 400 fo Movieaing 800 and 000 EachMovie wee conduced. As he imi of space he esus ae no epoed hee bu he ae consisen wih he esus epoed he poposed FMM mode go he bes pefomance in a cases. The evauaion meic used in ou epeimens was he common used mean absoue eo MAE which is he aveage absoue deviaion of he pediced aings fom he acua aings on iems he es uses have voed. MAE 27 Tes whee Tes is he numbe of he es aings. 5. Epeimen esus The fis se of epeimens is shown in Tabe 2 and Tabe 3. In addiion o he poposed FMM mode wo memobased and hee mode-based appoaches ae evauaed. The ae: he eason Coeaion Coefficien mehod CC he Veco Simiai mehod VS he aspec mode using eension Equaion 2 AM_a he aspec mode wih eension Equaion 3 AM_b and he esonai Diagnosis mode D. The wo-sided cuseing mode is no incuded because pevious sudies have shown ha is pefomance is subsania infeio o he aspec modes. The numbe of use casses and he numbe of iem casses in he FMM wee se o 0 and 20 fo uses and iems sepaae wihou much uning. Vaing he numbe of casses fom 5*0 o 20*40 gives us simia esus o hose epoed in Tabe 2 and 3. Accoding o Tabe 2 and 3 he poposed new FMM pefoms bee han a he ohe agoihms on a diffeen configuaions in ems of he MAE. Fuhemoe consisen wih ennock e a he D mehod achieves he second bes pefomance and is genea bee han he ohe fou mehods ecep AM_b on Each Movie wih 400 aining uses. The numbe of aspecs in he AM_a and AM_b wee uned fo he bes pefomance shown in iaic in Tabe 2 and 3. As fo he same numbe of aspecs AM_b has much moe paamees han AM_a hus i can be seen ha he opima numbe of aspecs in AM_b mode is smae han AM_a. Since he poposed FMM mode is simia o he aspec mode ecep fo he epici modeing of use and iem cuses we aibue he good pefomance of FMM o is abii of modeing he casses of uses and iems sepaae. Fuhemoe he diffeence beween he poposed mode and he wo-sided cuseing mode suggess ha i is beneficia no o assume ha each use iem beongs o a singe cass.

8 The second se of epeimens is shown in Tabe 4 and Tabe 5 whee we compae he pefomance of FMM wih and wihou he decouped modes DM. I is cea ha he combinaion of FMM mode wih DM mode oupefoms he basic FMM in a configuaions. Theefoe i is impoan o cuse uses wih simia pefeence paens insead of aing paens. I is ineesing o fuhe epoe efficien infeence and pedicion agoihms fo he gaphica mode in Figue 3 which is abe o simuaneous goup uses wih simia pefeence paens aing paens and iems wih simia chaaceisics and heefoe ma esu in even moe impovemen in he pedicion accuac. 6. Concusion and Fuue Wok aiion o cuseing echniques have been sudied inensive in he pevious wok fo coaboaive fieing. In his wok we poposed a foma gaphica mode fo coaboaive fieing named feibe miue mode FMM. The new mode ies o addess hee issues in coaboaive fieing: epici modeing boh casses of uses and iems b aking ino accoun hei coeaions; 2 aowing each use and iem o beong o muipe cuses simuaneous; 3 cuseing uses wih simia pefeence paens insead of aing paens. Epeimens on wo common esbeds wih sevea diffeen configuaions indicaed ha he poposed mode is abe o oupefom five ohe agoihms fo coaboaive fieing ask subsania. The combinaion mehod of he feibe miue mode and he decouped modes is ahe peimina. As fuue wok we pan o epoe bee efficien appoimaion agoihms fo infeence and pedicion wih he compe gaphica mode which can simuaneous goup uses wih simia pefeence paens aing paens and iems wih simia chaaceisics. Fina he poposed FMM mode is on appied and evauaed on he pobem of pedicing iem aing fo new uses; we hope o eend his mode fo ohe asks such as ecommending new iems o known uses in he fuhe wok. Acknowedgemens We hank Chengiang hai fo his hepfu discussion au Ogivie and Jamie Caan fo hei usefu commens and hep o impove he Engish in his pape. efeences Basu C. & Hish H ecommendaion as cassificaion: Using socia and conen-based infomaion in ecommendaion. In he oceedings of Fifeenh Naiona Confeence on Aificia Ineigence. Beese J. S. Heckeman D. Kadie C Empiica Anasis of edicive Agohms fo Coaboaive Tabe 4. Epeimen esus MAE on he Movieaing Tesbed fo FMM and FMM pus Decouped modes DM. A smae vaue means a bee pefomance. Taining Uses Sie Agoihms 5 Iems 0 Iems 20 Iems FMM FMM+DM FMM FMM+DM Tabe 5. Epeimen esus MAE on he EachMovie Tesbed fo FMM and FMM pus Decouped modes. A smae vaue means a bee pefomance. Taining Uses Sie Agoihms 5 Iems 0 Iems 20 Iems FMM FMM+DM FMM FMM+DM Fieing. In he oceeding of he Foueenh Confeence on Unceain in Aificia Ineigence. O Conno M. & Heocke Jon Cuseing Iems fo Coaboaive Fieing. In he oceedings of SIGI-200 Wokshop on ecommende Ssems New Oeans A. Dempse A.. aid N. M. & ubin D. B Maimum ikeihood fom incompee daa via he EM agoihm. Jouna of he oa Saisica Socie B39: -38. Hofmann T. & uicha J aen Cass Modes fo Coaboaive Fieing. In he oceedings of Inenaiona Join Confeence on Aificia Ineigence. Hofmann T. & uicha J Saisica modes fo co-occuence daa Technica epo. Aificia Ineigence aboao Memo 625 M.I.T. ennock D. M. Hovi E. awence S. & Gies C Coaboaive Fieing b esonai Diagosis: A Hbid Memo- and Mode-Based Appoach. In he oceeding of he Sieenh Confeence on Unceain in Aificia Ineigence. esnick. Iacovou N. Suchak M. Begsom. & ied J Goupens: An Open Achiecue fo Coaboaive Fieing of Nenews. In oceeding of he ACM 994 Confeence on Compue Suppoed Coopeaive Wok.