How To Make A Profit From A Website

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1 Mg Koledge-Shrg Stes for Vrl Mretg Mtthe Rchrdso d edro Dogos Deprtet of Coputer Scece d Egeerg Uversty of Wshgto Box 3535 Settle, WA {ttr,pedrod}@cs.shgto.edu ABSTRACT Vrl retg tes dvtge of etors of fluece og custoers to expesvely cheve lrge chges behvor. Our reserch sees to put t o frer footg by g these etors fro dt, buldg probblstc odels of the, d usg these odels to choose the best vrl retg pl. Koledge-shrg stes, here custoers reve products d dvse ech other, re fertle source for ths type of dt g. I ths pper e exted our prevous techques, chevg lrge reducto coputtol cost, d pply the to dt fro oledge-shrg ste. We opte the out of retg fuds spet o ech custoer, rther th ust g bry decso o hether to ret to h. We te to ccout the fct tht oledge of the etor s prtl, d tht gtherg tht oledge c tself hve cost. Our results sho the robustess d utlty of our pproch. Ctegores d Subect Descrptors H..8 [Dtbse Mgeet]: Dtbse Applctos dt g; I..6 [Artfcl Itellgece]: Lerg ducto; I.5. [tter Recogto]: Models sttstcl; J.4 [Coputer Applctos]: Socl d Behvorl Sceces Keyords robblstc odels, ler odels, drect retg, vrl retg, socl etors, oledge shrg ersso to e dgtl or hrd copes of ll or prt of ths or for persol or clssroo use s grted thout fee provded tht copes re ot de or dstrbuted for proft or coercl dvtge d tht copes ber ths otce d the full ctto o the frst pge. To copy otherse, to republsh, to post o servers or to redstrbute to lsts, requres pror specfc persso d/or fee. SIGKDD, Edoto, Albert, Cd. Copyrght ACM //7 $5... INTRODUCTION Mretg hs bee oe of the or pplctos of dt g sce the feld eerged. Typclly, the decso of hether or ot to ret to prtculr perso s bsed solely o ther chrcterstcs (drect retg), or those of the populto seget to hch they belog (ss retg). Ths ofte leds to suboptl retg decsos by ot tg to ccout the effect tht ebers of ret hve o ech other s purchsg decsos. I y rets, custoers re strogly flueced by the opos of ther peers. Vrl retg tes dvtge of ths to expesvely proote product by retg prrly to those th the strogest fluece the ret. The use of reltoshps betee people es vrl retg potetlly ore proftble th drect retg. Dt g techques hve bee successfully eployed for drect retg [9]. By buldg odels tht predct future purchsg behvor fro pst behvor, retg c be ore trgeted d led to creses proft [8][]. I prevous or [5], e shoed tht the se could be doe for vrl retg. By explctly odelg the ret s socl etor [4], e ere ble to use the fluece betee custoers to our dvtge to sgfctly crese profts. Vrl retg uses the custoers ret to proote product. Ths ord-of-outh dvertsg c be uch ore cost effectve th trdtol ethods sce t leverges the custoers theselves to crry out ost of the prootol effort. Further, people typclly trust d ct o recoedtos fro freds ore th fro the copy sellg the product. Exples of vrl retg re becog cresgly coo. A clssc exple of ths s the Hotl free el servce, hch gre fro ero to llo users 8 oths o scule dvertsg budget, ths to the cluso of prootol essge th the servce s URL every el set usg t [3]. Copettors usg covetol retg fred fr less ell. My rets, otbly those ssocted th forto goods (e.g., softre, ed, telecouctos, etc.) cot strog etor effects (o the ecoocs lterture s etor exterltes). I these, gorg the reltoshps betee custoers c led to severely sub-optl retg pl. I the presece of strog etor effects, t s crucl to cosder ot oly custoer s trsc vlue (hs vlue s custoer bsed o the products he s lely to purchse), but lso hs etor vlue. The etor vlue of custoer s hgh he he s expected to hve very postve fluece o others probbltes of purchsg the product. A custoer hose trsc vlue s less th the cost of retg y fct be orth retg to he hs etor vlue s cosdered. The edte effect of retg to h y be egtve, but the overll effect y be postve oce hs fluece o hs freds, ther flueces o ther freds, d so o s te to ccout. Further, custoer ho loos vluble bsed o trsc vlue loe y fct ot be orth retg to f he s expected to hve overll egtve effect o others the ret (e.g., perso ho teds to gve very lo product rtgs). Igorg the etor vlue c result correct retg decsos, especlly ret th strog etor effects. To estte the etor vlue of ts custoers, copy eeds to o the reltoshps betee the. Oe source of such forto s the Iteret, th ts plethor of cht roos, dscus-

2 so forus, d oledge-shrg eb stes. I these s foud elth of socl tercto, ofte product-relted, hch copy could use to gther forto o the reltoshps betee ts custoers. Koledge-shrg stes prtculr re ofte product-oreted. O these stes, forto bout product les d dsles, rtgs of qulty, bechrs, d coprsos re exchged, g the del source for dt bout custoer prefereces d terctos. I ths pper, e exted des fro our erler or [5] d pply the to the do of oledge-shrg stes. We sho ho to fd optl vrl retg pls, use cotuously vlued retg ctos, d reduce coputtol costs (Sectos d 3). I Sectos 4 d 5, e pply the odel to Epos, populr oledge-shrg ste. I prctce, the reltoshps betee custoers s ofte uo, but y be obted t soe cost. We troduce techque for retg such stuto d sho tht t perfors ell eve th very lted retg reserch fuds. We coclude th dscusso of relted or d future drectos.. THE MODEL Cosder set of potetl custoers, d let be Boole vrble tht tes the vlue f custoer buys the product beg reted, d otherse. Let the eghbors of be the custoers ho drectly fluece : N {,,,, } -{ }, here {,, }. The product s descrbed by set of ttrbutes Y{Y,,Y }. Let M be the retg cto tht s te for custoer. For exple, M could be Boole vrble, th M f the custoer s (sy) offered dscout, d M otherse. Altertvely, M could be cotuous vrble dctg the se of the dscout offered, or ol vrble dctg hch of severl possble ctos s te. Let M{M,,M } be the retg pl. The, for ll, e ll ssue tht ( { }, Y, ( N, Y, β ( Y, M ) + ( β ) N ( N, Y, ( Y, M ) s s terl probblty of purchsg the product. N ( N, Y, M ) s the effect tht s eghbors hve o h. β s sclr th β tht esures ho self-relt s. For y products, such s cellulr telephoes, ult-plyer coputer ges, d Iteret cht progrs, custoer s probblty of purchsg depeds strogly o hether hs freds hve lso purchsed the product. I prevous or [5] e odeled ths tercto th o-ler fucto. I ths pper, e eploy sple ler odel to pproxte ths effect: ( N, Y, () N N here represets ho uch custoer s flueced by hs eghbor, th d (Note, f N N ). Whle ot exct, e beleve t s resoble pproxto he the probbltes re ll sll, s s typclly the cse for retg dos. Ler odels ofte perfor ell, especlly he dt s sprse [4], d provde sgfct dvtges for coputto. Note tht e re odelg oly postve terctos betee custoers, hch e foud our prevous or to be the ost coo type. () Cobg Equtos d, e get ( N, Y, ( Y, M ) + ( β ) N β (3) For the purposes of ths pper, e ll be clcultg the optl retg pl for product tht hs ot yet bee troduced to the ret. I ths stuto, the stte of the eghbors ll ot be o, so e derve forul for coputg ( Y, M ). We frst su over ll possble eghbor sttes: ( Y, ( N, Y, ( N Y, N C ( N ) here C(N ) s the set of ll possble cofgurtos of the eghbors of, d hece Ñ s set of eghbor stte ssgets. Substtutg equto 3, e get: ( Y, β ( Y, M ) ( N Y, + N C ( N ) N C ( N ) ( β ) N N ( N Y, here Ñ s the vlue of specfed by Ñ. ( Y, M ) s depedet of Ñ, so the frst ter splfes to t. We sp the suto order the secod ter, d ote tht t s ero heever Ñ s ero. Ths leds to: ( β Y, Y, M ) + ( β ) N Y M ( (, ) N N C ( N ) th N Sce the er suto s over ll possble vlues of Ñ heever Ñ, t s equvlet to ( Y, M ), hece: ( Y, β ) ( Y, (4) ( Y, M ) + ( β N Becuse Equto 4 expresses the probbltes ( Y, M ) s fucto of theselves, t c be ppled tertvely to fd the, strtg fro sutble tl ssget. A turl choce for tlto s to use the terl probbltes ( Y, M ). The reter s gol s to fd the retg pl tht xes proft. For splcty, ssue tht M s Boole vector (.e., oly oe type of retg cto s beg cosdered, such s offerg the custoer gve dscout). Let c be the cost of retg to custoer (ssued costt), r be the reveue fro sellg the product to the custoer f o retg cto s perfored, d r be the reveue f retg s perfored. r d r ll be the se uless the retg cto cludes offerg dscout. Let f ( be the result of settg M to d levg the rest of M uchged, d slrly for f (. The expected lft proft fro retg to custoer solto (.e., gorg hs effect o other custoers) s the [3] EL ( Y, r ( Y, f ( ) r ( Y, f ( ) c

3 We lso refer to ths s the custoer s trsc vlue. Let M be the ull vector (ll eros). The globl lft proft tht results fro prtculr retg pl M s the EL( Y, [ r ( Y, r ( Y, M) c ] here r r d c c f M, d r r d c f M. A custoer s totl vlue s the globl lft proft fro retg to h: EL(Y, f () EL(Y, f (). A custoer s etor vlue s the dfferece betee hs totl d trsc vlues. A custoer th hgh etor vlue s oe ho, he reted to, drectly or drectly flueces y others to purchse. Our prevous or s bsed o ths Boole retg cse, but ths pper e explore cotuous vlued retg ctos s ell. The expected lft proft the cotuous cse s strghtforrd exteso of the Boole oe. Let be retg cto, th, d he o retg s perfored. Let c( be the cost of perforg the cto (th c()), d r( be the reveue obted f the product s purchsed. Let f ( be the result of settg M to d levg the rest of M uchged. The expected lft proft fro perforg retg cto o custoer solto s the EL ( Y, r( ( r() ( The globl lft proft s EL( Y, Y, f Y, f ( ) ( ) c( [ r( M ) ( Y, r () ( Y, M ) c( M )] 3. INFERENCE AND SEARCH Our gol s to fd the M tht xes EL(Y,. I our prevous or, e ssued retg ctos ere Boole, d heurstclly serched through the vst spce of possble retg pls. Becuse of the lerty of the odel preseted here (see Equto 3), the effect tht retg to perso hs o the rest of the etor (ther etor effect) s depedet of the retg ctos to other custoers. Fro custoer s etor effect, e c drectly copute hether he s orth retg to. Let the ( be the etor effect of custoer for product th ttrbutes Y. It s defed s the totl crese probblty of purchsg the etor (cludg ) tht results fro ut chge ( ): ( Y, M) ( Y ) (6) ( Y, M ) Sce ( s the se for y M, e defe t for M M. We c clculte ( usg the follog recursve forul (see the Appedx for proof) ( ) ( Y (7) Itutvely, custoer s etor effect s sply the effect tht he hs o people he flueces, tes ther effect o the etor. (5) ( s tlly set to for ll, the recursvely re-clculted usg equto 7 utl covergece (ote ths tes pproxtely ler te the uber of o-ero s). Eprclly, e foud t coverged qucly (- tertos). Note tht hle the etor vlue of custoer depeds o the retg scero, the etor effect does ot. The etor effect sply descrbes ho uch fluece custoer hs o the etor. The etor vlue depeds o the etor effect, the custoer s resposveess to retg, d the costs d reveues ssocted th the retg scero. Wth the etor effects hd, e c clculte the expected lft proft of retg to ech custoer. For coveece, e defe (, to be the edte chge custoer s probblty of purchsg he he s reted to th retg cto : (, β [ ( Y, M ( Y, M ) ] Fro Equto 6, d gve tht ( Y, M) vres lerly th ( Y, M ), the chge the probblty of purchsg cross the etre etor s the ( Y, M) ( ( ( (, Y, M ) Typclly, oly sll porto of the etor ll be reted to. Therefore, t s reltvely sfe to pproxte the crese reveue fro the etor due to retg to custoer s hs fluece o the etor ultpled by r(). The totl lft proft s ths crese reveue o the etor, plus the chge reveue fro custoer, us the cost of the retg cto: EL, totl ( Y, r() + [( ( ) (, ] [ r( ( Y, f ( ) r() ( Y, ] c( Notce tht ths pproxto s exct he r( s costt, hch s the cse y retg scero tht s dvertsgbsed (.e., f t does ot offer dscouts). Whe ths s the cse, the equto splfes to: EL, totl ( Y, r [( ( ) (, ] + r[ (, ] r ( (, c( c( (8) Wth Equto 8, e c drectly estte custoer s lft proft for y retg cto. Typclly, e ll t to fd the tht xes the lft proft. To do ths, e te the dervtve th respect to d set t equl to ero, resultg : d (, dc( r ( Y ) (9) d d Assug (, s dfferetble, ths llos us to drectly clculte the hch xes EL,totl (Y, hch, becuse our odel s ler, s the optl vlue for M the M tht

4 xes EL(Y,. Hece, fro the custoers etor effects, (, e c drectly clculte the optl retg pl. We o sho ho ths odel c be ppled to oledgeshrg stes. 4. MINING KNOWLEDGE-SHARING SITES Iteret use hs exploded over the pst decde. Mllos of people terct th ech other ole, d, y stces, those socl terctos re recorded rchves tht rech bc tety yers or ore. As result, there re y ole opportutes to e socl etors for the purposes of vrl retg. UseNet esgroups, IRC, stt essgg, ole forus, d el lg lsts re exples of possble sources. I ths pper, e cocetrte o oledge-shrg stes. O such stes, voluteers offer dvce, product rtgs, or help to other users, typclly for free. Socl tercto o oledge-shrg stes coes vrety of fors. Oe feture tht s ofte foud s soe for of explct trust betee users. For exple, t y stes, users rte reves ccordg to ho helpful or ccurte they re. O others, users drectly rte other users. Wthout flterg feture such s ths, oledge-shrg stes c qucly becoe red ccurte or pproprte reves. We hve chose to e Epos, possbly the best o oledge-shrg ste. O Epos, ebers subt product reves, cludg rtg (fro to 5 strs) for y of over oe hudred thousd products. As dded cetve, reveers re pd ech te oe of ther reves s red. Epos users terct th ech other both of the ys outled bove, by rtg reves, d lso by lstg reveers tht they trust. The etor of trust reltoshps betee users s clled the eb of trust, d s used by Epos to re-order the product reves such tht user frst sees reves by users tht they trust. The trust reltoshps betee users, d thus the etre eb of trust, c be obted by crlg through the pges of the dvdul users 3. Wth over 75 users d 5 edges ts eb of trust, d 586 reves over 4 products, Epos s del source for experets o socl etors d vrl retg. Iterestgly, e foud tht the dstrbuto of trust reltoshps the eb of trust s Zpf [5], s hs bee foud y socl etors [4]. Ths s evdece tht the eb of trust s represettve exple of socl etor, d thus s good bss for our study. A Zpf dstrbuto of trust s lso dctve of seed dstrbuto of etor vlues, d therefore of the potetl utlty of vrl retg. To pply our odel to Epos, e eeded to estte soe preters, such s the effect tht retg hs o custoer s probblty of purchsg, the self-relce fctor β, d the out of fluece betee custoers. I prctce, the retg reserch deprtet of copy, or the ters of the oledge-shrg ste tself, ould typclly hve the resources d ccess to custoers ecessry to experetlly de- See d Epos does ot provde lst of ll of ts users, so e seeded the crl th the top reveers ech product ctegory d folloed both trusts d trusted-by ls to fd other users. tere these preters. For stce, the effect tht retg hs o custoer could be esured by selectg users t rdo d recordg ther resposes (both he beg reted to d ot). The preters could be estted dvdully for ech user, or (requrg fr less dt) s the se for ll users, s s doe Chcerg d Hecer [3]. If ths s ot fesble, they could be set usg cobto of pror oledge d y deogrphc forto vlble. For Epos, e de the splfyg ssupto tht user s ore lely to purchse product f t s reveed by perso he trusts. Though ot requred by the odel, e cosdered ll trusted people to hve equl fluece, s there s o dt Epos to for otherse. Thus, N { such tht trusts } d / N for N. For the product ttrbute vector Y, e used sgle ttrbute: the product ctegory (fro oe of 5 top-level ctegores defed by Epos). The odel supports ore coplex ttrbute vectors. For exple, oe could ge usg the text descrpto of products, possbly ugeted by the product ctegory d sub-ctegory. We pl to explore ther effect future or. All tht reed to defe s ( Y, M ), hch e estted usg ïve Byes odel[4] for s fucto of Y d M. ( Y ) ( M ) ( ) ( Y, M ) ( Y ) ( M ) ( ) ( ( M ) ( ( M ) We used ïve Byes odel for ( Y ). We equted reveg product th purchsg t 4, so trg the odel s sply tter of coutg. I the cse of Epos, esurg the effectveess of retg o the users s ot possble for us. We expected retg to hve lrger effect o custoer ho s lredy cled to purchse the product, so e folloed our prevous or d set ( M ) so s to obt (for the Boole retg scero): M ) { α ( M ),} () ( here α > s preter tht specfes the gtude of the retg effect EERIMENTS We bult the odel bsed o Epos dt, s dscussed bove, d used t to gther eprcl results. For ll of the experets, e used ust oe of the 5 product ctegores, Kds & Fly, s t hd the ost reves per product (., o verge) d 4 We expect tht ore users purchse the product th reve t. Hoever, purchsers ho do ot reve hve o ddtol effect o the etor, so og the rto of purchsers to reveers ould sply scle the results. The results ould be ffected f e e, per user, the probblty of purchsg vs. reveg, but ths forto s ot vlble to us. 5 To fully specfy ( M ) e used the ddtol costrt tht ( Y, M ) ( Y, M ). Wth the vlues of α e used t s lys possble to stsfy Equto d ths costrt sulteously.

5 reves per perso ho subtted t lest oe reve the ctegory (5.8, o verge). We frst tested the Boole retg cse. We hypothesed sple dvertsg stuto th α, r, r, hch et reveues ere uts of the uber of products sold, d perso s terl probblty of purchsg product doubled fter beg dvertsed to 6. I erler or, e vred α d foud tht, hle t ffected the scle of the results, t hd lttle effect o the qulttve ture of the. Thus, for ths pper, e fxed α d sted vred other chrcterstcs of the odel. We hd o dt to estte users self-relce, so e sply chose to set β.5 for ll custoers. To cobt dt sprseess, ( Y ) s soothed usg -estte th d the populto verge s the pror. These preters ere ll chose before rug y experets. Norled Netor Vlue R Tble : roft results for Boole retg scero for vrous costs of retg. α, r, r c. c. c. No Mretg Drect Mretg Vrl Mretg rofts d Netor Vlues Vrl retg resulted cosderble crese proft over drect retg (see Tble ). Notce tht he the cost of retg s sgfct frcto of the reveue, the drect reter ll choose to ret to o oe becuse the cost of retg exceeds the expected reveue fro the custoer (sce the custoers flueces o ech other re beg gored). As ths scero llustrtes, ssug the odel s ccurte, vrl retg ll lys perfor t lest s ell s drect retg, ofte outperforg t by substtl rg. We esured the etor vlue of ll of the custoers. Fgure shos the 5 hghest etor vlues (out of 75888) decresg order. The ut of vlue ths grph s the verge reveue tht ould be obted by retg to custoer solto, thout costs or dscouts. Thus, etor vlue of for gve custoer ples tht by retg to h e essetlly get free retg to ddtol custoers. The scle of the grph depeds o the retg scero (e.g., etor vlues crese th α), but the shpe geerlly res the se. The fgure shos tht fe users hve very hgh etor vlue. Ths s the del stuto for the type of trgeted vrl retg e propose, sce e c effectvely ret to y people hle currg oly the expese of retg to those fe. A custoer th hgh etor vlue s oe ho: () Is lely to purchse the product, d thus s ore ffected by the retg, d () s trusted by y other people the etor, ho ted 6 I prevous or e vred the vlue of α d foud tht, hle t ffected the scle of results, they reed qulttvely slr. Fgure : Typcl dstrbuto of etor vlue. to hve lo β, d ho lso hve chrcterstc, d so o recursvely. For stce, the custoer th the hghest etor vlue (,) flueces 784 people, d hs probblty of purchsg of.3, hch s 3 tes tht of the verge perso. 5. Speed The ler odel troduced ths pper hs treedous speed dvtges over o-ler odel such s tht troduced our prevous or. Becuse of the depedece tht lerty provdes, e re ble to sulteously clculte the etor vlue for ll custoers. The etor vlue s depedet of the retg ctos beg perfored o others, hch llos us to fd the optl retg pl 7 thout perforg heurstc serch over pls. It ould te pproxtely hours to perfor the sgle-pss serch (the fstest of the heurstc serch ethods troduced our prevous or) th ths odel, or bout -5 utes f e e pproxtos the ferece. I cotrst, the ler odel tes.5 secods to fd the optl retg pl. At these speeds, our odel could be used to fd optl retg pls for rets volvg hudreds of llos of custoers ust hours. 5.3 Cotuous Mretg Actos Cotuous-vlued retg ctos (M [,]) llo the reter to better opte the retg pl tlorg the cto for ech perso specfclly to hs chrcterstcs. Our freor llos for y fucto to be used to odel ( Y, M ), s log s t s dfferetble M. As the Boole cse, e hve chose to odel the effect of retg s ultplctve fctor o the terl probblty of purchsg: ( M α ( ( M ) α( could be y dfferetble fucto, d e ssue α(). c( lso could be y dfferetble fucto. We hve chose c(c such tht the cost of retg s drectly proportol to the out of retg beg perfored. 7 The pl s optl f r r (or f r( s costt the cotuous retg sceros). If r <r the the pl overesttes the reveues fro fluece o the etor, potetlly resultg sub-optl retg pl. I our experece, ths overestto rged fro % to % of the profts. We thus beleve the resultg pl s stll erly optl.

6 α( Mretg Acto ( Fgure : Mretg effect vs. retg cto. We beleve expoetlly syptotc fucto for α( s resoble; t odels the pheoeo of dshg returs (.e., the ore oey tht s spet o retg, the less proveet s derved fro t). We lso expereted th logrthc d verse polyol fuctos, hch gve slr results. The fucto e used s: α( α + ( α ) e λ Note tht α(), d α( α s. The preter λ ffects the curvture of the fucto; α( coverges to α ore qucly th lrge λ. I the experets belo, e used λ5, hch s lrge eough tht α() α, yet lo eough tht α( does ot coverge to α too qucly. The resultg curve, for α, s sho Fgure. Fro equto 9, e c fd the optl retg cto for ech custoer dc( r( β ( d Y, M c r ( β λ( α ) e λ c l r ( βλ( α ) ( λ d( α( ) ) d Y, M ) The secod dervtve s egtve, plyg the pot s xu. We r the se experets s the Boole cse, th α so tht retg fully to custoer ll double ther terl probblty of purchsg the product, s before. The results re preseted Tble. I ll three sceros, d for both drect d vrl retg, cotuous retg ctos resulted hgher lft proft th Boole ctos, soetes by very sgfct out. Vrl retg lso cotued to cosstetly outperfor drect retg. The cresed lft proft s due to to fctors: () At lo, the α( curve provdes ore fvorble rto of retg effect to cost, d () tlorg the retg cto for ech custoer llos us to opte the trdeoff betee the cost d beeft of retg o per custoer bss. Tble : roft results for cotuous retg scero for vrous costs of retg. α, r(, λ5 c. c. c. No Mretg Drect Mretg Vrl Mretg Lft over Boole Vrl Mretg 3.89 (4.8%).69 (.8%).5 (3.4%) To verfy tht fctor () s ot the sole cuse of the crese proft, e r Boole retg experets th αα( d cc( for rgg fro to. Dog so sultes copy hch globlly optes ts choce of retg cto, but stll perfors tht se (or o) cto o ech custoer. The xu relble profts ths cse ere 49.9, 6.6, d 7.3 for c of.,., d.. These results sho tht tlorg the retg cto for ech custoer s deed sgfct cuse of the crese profts derved fro the cotuous retg cse. Oe terestg questo s ht hppes f the retg effect fucto α( s ler, α( α. I ths cse, cotuous-vlued retg reduces to Boole retg. If t ould be proftble to ret to custoer soe (>), the the beeft of retg to h ust be hgher th the cost for y (sce both the cost d the beeft re ler), d t ould thus dvtgeous to ret to h the xu possble (. 5.4 Icoplete Netor Koledge So fr, e hve cosdered oly rets here the etre socl etor betee custoers s o. Ths s ofte ot the cse. I fct, ost copes tody hve lttle or o oledge of the ctul reltoshps betee ther custoers. I such stuto, copes y sply choose to use drect retg, but f they do, they ll lely lose proft opportutes, s deostrted erler sectos. I the follog sectos, e ll deostrte tht eve th lttle etor oledge, our vrl retg ethods stll outperfor drect retg. I ll of the experets tht follo, e used cotuous-vlued retg ctos, th the se preters s those used for Secto 5.3 (Tble ) d c Vrl retg s robust We sulted prtl oledge by rdoly reovg ebers fro the eghbor sets, hch correspods to rdoly reovg edges fro the socl etor. Ths s the stuto copy ould be f they hd oly rdo sple of the eghbor reltos betee custoers. We devsed the optl retg pl o the coplete etor, d the tested ths pl o the coplete etor, hch sultes the rel-orld. Nturlly, he o edges re o, vrl retg s equvlet to drect retg.

7 Addtol Lft I roft bove Drect Mretg Frcto of edges o Actul Estted Fgure 3: Actul d estted dfferece betee vrl retg d drect retg profts th oly prtl etor oledge. I Fgure 3 ( Actul ), e sho the dfferece proft betee drect d vrl retg for prtlly o etors. Surprsgly, the copy c cheve 69% of the lft proft og oly 5% of the edges the etor. Further, the lgorth cosderbly uderesttes the lft proft tht ll result (Fgure 3, Estted ), eg tht for copy th oly prtl etor oledge, ot oly re vrl retg pls robust but the ctul results of vrl retg ll be sgfctly better th the lgorth esttes. We hypothese tht ths robustess ll occur heever the edges re ssg t rdo (or pproxtely so), resultg correlto betee the uber of people ho trust gve perso the prtl etor d the uber ho trust h the true etor. A custoer ho ppers to hve hgh etor vlue the prtl etor s lely to hve hgh etor vlue the full etor, d ould thus be chose to be reted to. We lso beleve tht the lgorth could use estte of the frcto of edges tht re ssg to costruct eve better vrl retg pl; e pl to vestgte ths future or Acqurg e etor oledge I y stces, copy ll hve lttle or o oledge bout the reltoshps betee ts custoers, but y be llg to sped retg reserch fuds to cqure t. More oledge bout the flueces betee custoers ll llo the copy to for retg pl th hgher lft proft. If the copy could copute the vlue of forto [8] of og the eghbors of ech custoer, t could the e decsotheoretc choce of hch, d ho y, custoers to query. The cqusto of eghbor reltos could be doe y ys. For the purposes of ths pper, e ssue tht t s doe by selectg user to query, spedg oey to persude h to provde lst of the people he trusts, selectg other user to query, d so o. We ssue the copy hs fxed out of oey t s llg to sped for ths, d tht the cost of queryg user s costt. The terestg proble s thus ot ho y users to query, but ho to select the subset of users to query tht leds to the ost proft. Lft I roft By Netor Effect Rdo Custoers Quered Fgure 4: Lft proft (o the full etor) for the vrl retg pl hch the gve uber of custoers hs bee quered for ther eghbor forto. A custoer th hgh etor effect hs lrge fluece o the etor, d s thus oe tht e sh to fluece to purchse the product. Aprt fro drectly retg to the custoer, e c drectly fluece h by retg to those tht he trusts, hch e c dscover by queryg h. Oe estte for custoer s etor effect o the full etor s hs etor effect o the prtl etor. We thus query the custoer th the hghest etor effect o the prtl etor, reclculte etor effects th the e forto, query the ext custoer th hghest etor effect, d so o utl the retg fuds hve bee spet. We perfored ths experet, strtg th etor cotg o eghbor forto 8. Fgure 4 shos the resultg lft proft, copred to rdoly selectg custoers to query. Our ethod perfors ell, lftg profts order of gtude ore th rdo choce ould he custoers re quered, d by lost 3 tes the lft cheved by rdo choce he % of the custoers re quered. We ust re-clculte the custoers etor effects ech te e query user. We c drstclly speed ths up by queryg the custoers th hghest etor effect t ech terto, th potetl loss of ccurcy. Iterestgly, the lft proft he selectg custoers t te s oly (o verge).8 less th he selectg oe t te, eglgble out copred to the lft proft tself. Sce t tes / th the te to ru, ths pproxto could be used to e oledge cqusto trctble for o-ler odels, or for rets of tes of llos of custoers. I future or, e ould le to fd esure tht esttes the crese EL of queryg oe ore user, thus forg the copy he to stop cqurg etor oledge. Ths ould llo us to opte the overll proft (lft proft us fuds spet to cqure etor oledge). We beleve such esure could be fored fro the EL, estte of the uber of ssg edges, d other sttstcs o the prtl etor. 8 The frst custoers to query re therefore chose t rdo.

8 6. RELATED WORK I our prevous or [5], e ed collbortve flterg syste to deostrte the dvtges of our vrl retg pproch over drect or ss retg. There, e used ore coplcted, pecese ler fucto over product rtgs to detere the flueces of custoers o ech other. I ths pper, e used odel th stroger lerty ssuptos to cheve greter sclblty. A dsdvtge of our prevous or s tht t requred full oledge of etor structure, d restrcted the reter to selectg Boole retg ctos. Both of these lttos ere ddressed d overcoe ths pper. Iterestgly, the coputto of etor effect (see Equto 7) s very slr to the ger[] lgorth, used by Google[] for deterg portt eb pges. I ger, eb pge s vlued hghly f y hghly vlued pges pot to t. Slrly, vrl retg custoer s vlued hghly f he flueces y hghly vlued custoers. The coputto s equvlet to fdg the prry egevector of the trx W, here W ( for ger). The etor effect of custoer s lso proportol to the probblty tht rdo ler, ho rdoly trverses the ls of fluece the etor bcrds, s t tht custoer. Also relted s the HITS[5] lgorth, hch ould fd bprtte trusts/trusted-by sub-grphs the eb of trust. Iterestgly, socl etors, the World-Wde Web, d y turlly occurrg etors ll exhbt Zpf, or scle free chrcterstcs, d hve bee the topc of uch recet reserch [7] []. Socl etors hve bee the obect of uch reserch. Oe clssc pper s tht by Mlgr [], hch estted tht every perso the orld s oly sx cqutces y fro every other. Soe recet socl etor reserch uses the Iteret s source of dt. For stce, Schrt d Wood [3] ed socl reltoshps fro el logs, the ReferrlWeb proect ed socl etor fro de vrety of publcly-vlble ole forto [4], d the COBOT proect gthered socl sttstcs fro prtcpt terctos the LbdMoo MUD []. Our etor s ed fro oledge-shrg ste. A good overve of Epos d other stes le t c be foud Fruefelder [6]. Severl reserchers hve studed the proble of esttg custoer s lfete vlue fro dt [], geerlly focusg o vrbles le dvdul s expected teure s custoer [9] d future frequecy of purchses [7]. Netors of custoers hve receved soe tteto the retg lterture [] but ost of these studes re purely qulttve, or volve very sll dt sets d overly splfed odels. Krchrdt [6] proposes odel for optg hch custoers to offer free sple of product to, but the odel oly cosders the pct o the custoer s edte freds, ssues the relevt probbltes re the se for ll custoers, d s oly ppled to de-up etor th seve odes. 7. FUTURE WORK We hve developed odels for vrl retg o socl etors ed fro rel-orld dt. There re y drectos hch these odels, or ther use, could be exteded. I ths secto, e descrbe soe of the oes. I ths pper, e ed etor fro sgle source. I geerl, ultple sources of relevt forto ll be vlble; the ReferrlWeb [4] proect exeplfed ther use. Methods for cobg dverse forto to soud represetto of the uderlyg fluece ptters re thus portt re for reserch. Here, e cosdered oly costt r(. I prelry experets, decresg r( cused the lgorth to soeht overestte the lft proft tht ould result fro prtculr retg pl, therefore lely ledg to sub-optl retg pl (though t stll outperfored drect retg). I future or, e ould le to vestgte ethods for hdlg vrble r(, hch y volve, for stce, correcto fctor bsed o the expected uber of custoers tht ll be reted to. We hve troduced ethods for developg retg pl he the structure of the etor s uo or oly prtlly o, but there re stll y drectos hch the ethods could be exteded. I prtculr, e ould le to explore the effect of hvg bsed etor sple o the resultg vrl retg pl. Kog ho the sple s bsed should led to better retg pls. Also, th ore forto t y be possble to e ore tellget selectos bout hch users to query. All forto o bout user (e.g., deogrphc chrcterstcs, pst purchsg behvor, d prtl oledge bout trusts/trusted-by reltos) could be used to estte the vlue of queryg h. We ould le to further develop the pplcto of the theory of vlue of forto [8] to optg the trdeoff betee the cost d expected beefts of cqurg oledge bout the etor. Ths pper cosdered g retg decsos t specfc pot te. A ore sophstcted ltertve ould be to pl retg strtegy by explctly sultg the sequetl dopto of product by custoers gve dfferet tervetos t dfferet tes, d dptg the strtegy s e dt o custoer respose rrves. A further te-depedet spect of the proble s tht socl etors re ot sttc; they evolve, d prtculrly o the Iteret c do so qute rpdly. Soe of the lrgest opportutes y le odelg d tg dvtge of ths evoluto. If the etor evoluto s uderstood, t y be possble to ffect the structure tself, drvg the etor tord oe hch hs hgher proft potetl. We ould lso le to vestgte further the lgorthc slrtes betee vrl retg d eb pge rg lgorths such s ger[] d HITS[5]. Applyg the techques d lessos lered vrl retg to the eb do, or vce vers, could result e sghts to the probles foud ech. For stce, recet or o g sgfct Web subgrphs such s bprtte cores, clques d eb rgs (e.g., [7]) y be pplcble to vrl retg. Ther techques could possbly be used to study etor sub-structures d detfy those th the hghest proft potetl. 8. CONCLUSION Ths pper uses dt g to prove vrl retg. We pply our techques to dt ed fro rel-orld oledgeshrg ste, d sho tht they scle effcetly to etors of hudreds of llos of custoers. We exted our techques to hdle cotuously vrble retg ctos d prtl etor oledge. Our results sho the prose of our pproch.

9 9. ACKNOWLEDGEMENTS Ths reserch s prtly fuded by NSF CAREER d IBM Fculty rds to the secod uthor.. REFERENCES [] A. L. Brbás, R. Albert, d H. Jog. Scle-free chrcterstcs of rdo etors: The topology of the World Wde Web. hysc A, 8:69-77,. [] S. Br d L. ge. The toy of lrge-scle hypertextul Web serch ege. I roceedgs of the Seveth Itertol World Wde Web Coferece, Brsbe, Austrl, 998. Elsever. [3] D. M. Chcerg d D. Hecer. A decso theoretc pproch to trgeted dvertsg. I roceedgs of the Sxteeth Aul Coferece o Ucertty Artfcl Itellgece, Stford, CA,. Morg Kuf. [4]. Dogos d M.. O the optlty of the sple Byes clssfer uder ero-oe loss. Mche Lerg, 9:3-3, 997. [5]. Dogos d M. Rchrdso. Mg the Netor Vlue of Custoers. I roceedgs of the Seveth Itertol Coferece o Koledge Dscovery d Dt Mg, pges 57-66, S Frcsco, CA,. ACM ress. [6] M. Fruefelder. Revege of the o-t-lls: Isde the Web s free-dvce revoluto. Wred 8(7):44-58,. [7] K. Gelbrch d R. Nhedeh. Vlue Mer: A dt g evroet for the clculto of the custoer lfete vlue th pplcto to the utootve dustry. I roceedgs of the Eleveth Europe Coferece o Mche Lerg, pges 54-6, Brcelo, Sp,. Sprger. [8] R. A. Hord. Iforto vlue theory. IEEE Trsctos o Systes Scece d Cyberetcs, SSC-: [9] A. M. Hughes. The Coplete Dtbse Mreter: Secod- Geerto Strteges d Techques for Tppg the oer of you Custoer Dtbse. Ir, Chcgo, IL, 996. [] D. Icobucc, edtor. Netors Mretg. Sge, Thousd Os, CA, 996. [] C. L. Isbell, Jr., M. Kers, D. Kor, S. Sgh, d. Stoe. Cobot LbdMOO: A socl sttstcs get. I roceedgs of the Seveteeth Ntol Coferece o Artfcl Itellgece, pges 36-4, Aust, T,. AAAI ress. [] D. R. Jcso. Strtegc pplcto of custoer lfete vlue drect retg. Jourl of Trgetg, Mesureet d Alyss for Mretg, :9-7, 994. [3] S. Jurvetso. Wht exctly s vrl retg? Red Herrg, 78:-,. [4] H. Kut, B. Sel, d M. Shh. ReferrlWeb: Cobg socl etors d collbortve flterg. Couctos of the ACM, 4(3):63-66, 997. [5] J. M. Kleberg. Authorttve sources hyperled evroet. I roceedgs of the Nth Aul ACM-SIAM Syposu o Dscrete Algorths, pges , Bltore, MD, 998. ACM ress. [6] D. Krchrdt. Structurl leverge retg. I D. Icobucc, edtor, Netors Mretg, pges Sge, Thousd Os, CA, 996. [7] R. Kur,. Rghv, S. Rgopl, d A. Tos. Extrctg lrge-scle oledge bses fro the Web. I roceedgs of the Tety-Ffth Itertol Coferece o Very Lrge Dtbses, pges , Edburgh, Scotld, 999. Morg Kuf. [8] C.. Lg d C. L. Dt g for drect retg: robles d solutos. I roceedgs of the Fourth Itertol Coferece o Koledge Dscovery d Dt Mg, pges 73-79, Ne Yor, NY, 998. AAAI ress. [9] D. R. M, J. Dre, A. Bet, d. Dtt. Sttstcs d dt g techques for lfete vlue odelg. I roceedgs of the Ffth ACM SIGKDD Itertol Coferece o Koledge Dscovery d Dt Mg, pges 94-3, Ne Yor, NY, 999. ACM ress. [] S. Mlgr. The sll orld proble. sychology Tody, :6-67, 967. [] L. ge, S. Br, R. Mot, d T. Wogrd. The ger ctto rg: Brgg order to the eb. Techcl Report, Stford Uversty, Stford, CA [] G. tetsy-shpro d B. Msd. Esttg cpg beefts d odelg lft. I roceedgs of the Ffth ACM SIGKDD Itertol Coferece o Koledge Dscovery d Dt Mg, pges 85-93, S Dego, CA, 999. ACM ress. [3] M. F. Schrt d D. C. M. Wood. Dscoverg shred terests usg grph lyss. Couctos of the ACM, 36(8):78-8, 993. [4] S. Wsser d K. Fust. Socl Netor Alyss: Methods d Applctos. Cbrdge Uversty ress, Cbrdge, UK, 994. [5] G. K. Zpf. Hu Behvor d the rcple of Lest Effort. Addso-Wesley, Bosto, MA, AENDI I ths ppedx, e gve proof for Equto 7: ( Y ) ( As ths s tertve equto, e detfy hch terto e re o by super-scrpt. Let (Y ) d ( Y, be the th estte of custoer s etor effect d probblty of purchsg, respectvely, d let ( Y, M ) sce o the th terto o etor effect s te to ccout. For ottol coveece, e lso defe ( β )

10 The tertve updte fro Equto 4 s: + M ), ( Y β Thus, Note tht f f Also ote, fro Equto 6, e hve d lso We frst ll prove by ducto tht for () We frst sho ths s true for the cse here : We o prove Equto s true for f e ssue t s true for -: Ths copletes the proof of Equto. We ll o prove by ducto tht for () We frst prove tht the ducto hypothess s true for the cse here : We o prove Equto s true for f e ssue t s true for -. By urollg the recurso, e obt Fro the defto of, d fro Equto : reg s, s - for -, d s -, e obt: We hve sho tht. If ths recurso s terted utl t reches fxed pot, the resultg vlues for stsfy ) ( ) ( Y Y Ths copletes the proof of Equto 7.